Algebra QBA 1 Review Short Answer 1. Juan scored 26 points in the first half of the basketball game, and he scored n points in the second half of the game. Write an expression to determine the number of points he scored in all. Then, find the number of points he scored in all if he scored 18 points in the second half of the game. 2. Salvador has saved 130 sand dollars and wants to give them away equally to n friends. Write an expression to show how many sand dollars each of Salvador s friends will receive. Then, find the total number of sand dollars each of Salvador s friends will get if Salvador gives them to 10 friends. 3. Isabel reads 15 books from the library each month for y months in a row. Write an expression to show how many books Isabel read in all. Then, find the number of books Isabel read if she read for 12 months. 4. Solve. Check your answer. 5. Solve. Check your answer. 6. Solve 14 + s = 32. 7. A toy company's total payment for salaries for the first two months of 2005 is $21,894. Write and solve an equation to find the salaries for the second month if the first month s salaries are $10,205. 8. The range of a set of scores is 23, and the lowest score is 33. Write and solve an equation to find the highest score. (Hint: In a data set, the range is the difference between the highest and the lowest values.) 9. Solve. Check your answer. 10. Solve 3n = 42. Check your answer. 11. Solve. 12. Solve. 18. Solve. 19. A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company? 13. Solve. 14. Solve. 15. Devon pays $24.95 for her roller skates. After that she pays $3.95 for each visit to the roller rink. What is the greatest number of visits she can afford if the total amount she spends cannot be more than $76.30? 16. The formula gives the profit p when a number of items n are each sold at a cost c and expenses e are subtracted. If,, and, what is the value of c? 17. Solve. 20. A professional cyclist is training for the Tour de France. What was his average speed in miles per hour if he rode the 120 miles from Laval to Blois in 4.7 hours? Use the formula, and round your answer to the nearest tenth. 21. The formula for the resistance of a conductor with voltage V and current I is. Solve for V.
22. Solve for x. 23. To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n represent the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will result in a swimmer making the team. Graph the solution. 24. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can spend the remainder of the money on music. Write an inequality to show how much he can spend on music. Then, graph the inequality. 25. Carlotta subscribes to the HotBurn music service. She can download no more than 11 song files per week. Carlotta has already downloaded 8 song files this week. Write, solve, and graph an inequality to show how many more songs Carlotta can download. 26. Denise has $365 in her saving account. She wants to save at least $635. Write and solve an inequality to determine how much more money Denise must save to reach her goal. Let d represent the amount of money in dollars Denise must save to reach her goal. 27. Marco s Drama class is performing a play. He wants to buy as many tickets as he can afford. If tickets cost $2.50 each and he has $14.75 to spend, how many tickets can he buy? 28. Solve the inequality z + 8 3z 4 and graph the solutions. 29. A family travels to Bryce Canyon for three days. On the first day, they drove 150 miles. On the second day, they drove 190 miles. What is the least number of miles they drove on the third day if their average number of miles per day was at least 180? 30. Mrs. Williams is deciding between two field trips for her class. The Science Center charges $135 plus $3 per student. The Dino Discovery Museum simply charges $6 per student. For how many students will the Science Center charge less than the Dino Discovery Museum? 31. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if there are at least 100 people on the plane. Write a compound inequality to show the possible number of people in a flight on a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions. 32. Tell whether the ordered pair (5, 3) is a solution of the system. 34. The Fun Guys game rental store charges an annual fee of $5 plus $5.50 per game rented. The Game Bank charges an annual fee of $17 plus $2.50 per game. For how many game rentals will the cost be the same at both stores? What is that cost? 33. Solve the system by graphing. 35. If the pattern in the table continues, in what month will the number of sales of CDs and movie tickets be the same? What number will that be? Total Number Sold Month 1 2 3 4 CDs 700 685 670 655 Movie tickets 100 145 190 235
36. Solve by substitution. Express your answer as an ordered pair. 37. Solve by substitution. Express your answer as an ordered pair. 38. Janice is going on vacation and needs to leave her dog at a kennel. Nguyen s Kennel charges $15 per day plus $20 for a processing fee. The Pup Palace Kennel charges $12 per day, and has a $35 processing fee. After how many days is the Pup Palace Kennel cheaper than Nguyen s Kennel? 39. Solve by elimination. Express your answer as an ordered pair. 40. Solve by elimination. Express your answer as an ordered pair. 41. Solve by elimination. Express your answer as an ordered pair. 42. At the local pet store, zebra fish cost $2.10 each and neon tetras cost $1.85 each. If Marsha bought 13 fish for a total cost of $25.80, not including tax, how many of each type of fish did she buy?
Algebra QBA 1 Review Answer Section SHORT ANSWER 1. ANS: 26 + n; 44 points The expression 26 + n models the number of points Juan scored in all. Evaluate 26 + n for n = 18. 26 + 18 = 44 If Juan scored 18 points in the second half of the game, then he scored 44 points in all. PTS: 1 DIF: 2 REF: 0ef4d6a2-4683-11df-9c7d-001185f0d2ea OBJ: 1-1.4 Application NAT: NT.CCSS.MTH.10.9-12.A.SSE.1 STA: MCC9-12.A.CED.1 LOC: MTH.C.10.05.02.02.013 MTH.C.10.05.02.02.019 TOP: 1-1 Variables and Expressions KEY: algebraic expression word problem operation DOK: DOK 3 2. ANS: ; 13 sand dollars The expression Evaluate for n = 10. = 13 models the number of sand dollars each of Salvador s friends will receive. If Salvador gives 130 sand dollars to 10 friends, each friend will get 13 sand dollars. PTS: 1 DIF: 2 REF: 0ef4fdb2-4683-11df-9c7d-001185f0d2ea OBJ: 1-1.4 Application NAT: NT.CCSS.MTH.10.9-12.A.SSE.1 STA: MCC9-12.A.SSE.1 MCC9-12.A.CED.1 LOC: MTH.C.10.05.02.02.013 MTH.C.10.05.02.02.019 TOP: 1-1 Variables and Expressions KEY: algebraic expression word problem operation DOK: DOK 3 3. ANS: 15y; 180 books The expression 15y models the number books Isabel read in all. Evaluate 15y for y = 12. 15(12) = 180 If Isabel read for 12 months, then that means Isabel read 180 books. PTS: 1 DIF: 2 REF: 0ef738fe-4683-11df-9c7d-001185f0d2ea OBJ: 1-1.4 Application NAT: NT.CCSS.MTH.10.9-12.A.SSE.1 STA: MCC9-12.A.SSE.1a LOC: MTH.C.10.05.02.02.013 MTH.C.10.05.02.02.019 TOP: 1-1 Variables and Expressions KEY: algebraic expression word problem operation DOK: DOK 3
4. ANS: p = 22 Since 6 is subtracted from p, add 6 to both sides to undo the subtraction. Check: To check your solution, substitute 22 for p in the original equation. PTS: 1 DIF: 1 REF: 0f88cffa-4683-11df-9c7d-001185f0d2ea OBJ: 1-2.1 Solving Equations by Using Addition NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.004 TOP: 1-2 Solving Equations by Adding or Subtracting KEY: equation solving subtraction 5. ANS: s = 42 Since 6 is added to s, subtract 6 from both sides to undo the addition. Check: To check your solution, substitute 42 for s in the original equation. PTS: 1 DIF: 1 REF: 0f8b0b46-4683-11df-9c7d-001185f0d2ea OBJ: 1-2.2 Solving Equations by Using Subtraction NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.005 TOP: 1-2 Solving Equations by Adding or Subtracting KEY: equation solving addition 6. ANS: s = 46 When something is added to the variable, add its opposite to both sides of the equation to isolate the variable. Here, 14 is added to the variable, so add 14 to both sides of the equation to isolate s. PTS: 1 DIF: 1 REF: 0f8d6da2-4683-11df-9c7d-001185f0d2ea OBJ: 1-2.3 Solving Equations by Adding the Opposite NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.004 TOP: 1-2 Solving Equations by Adding or Subtracting KEY: equation solving subtraction
7. ANS: The salaries for the second month are $11,689. First month salaries Added to Second month salaries is 21,894 b + x = 21,894 b + x = 21,894 10,205 + x = 21,894 10,205 10,205 Write an equation to represent the relationship. Substitute 10,205 for b. Since 10,205 is added to x, subtract 10,205 from both sides to undo the addition. The salaries for the second month are $11,689. PTS: 1 DIF: 2 REF: 0f8d94b2-4683-11df-9c7d-001185f0d2ea OBJ: 1-2.4 Application NAT: NT.CCSS.MTH.10.9-12.A.CED.1 NT.CCSS.MTH.10.9-12.A.REI.3 STA: MCC9-12.A.CED.1 MCC9-12.A.REI.3 LOC: MTH.C.10.06.01.009 MTH.C.10.06.02.01.005 TOP: 1-2 Solving Equations by Adding or Subtracting DOK: DOK 3 8. ANS: KEY: equation solving addition subtraction The highest score is 56. highest score minus lowest score equals score range h l = 23 Write an equation to represent the relationship. Substitute 33 for l. Solve the equation. PTS: 1 DIF: 3 REF: 0f8fcffe-4683-11df-9c7d-001185f0d2ea NAT: NT.CCSS.MTH.10.9-12.A.CED.1 NT.CCSS.MTH.10.9-12.A.REI.3 STA: MCC9-12.A.CED.1 MCC9-12.A.REI.3 LOC: MTH.C.10.06.01.009 MTH.C.10.06.02.01.004 TOP: 1-2 Solving Equations by Adding or Subtracting KEY: equation solving addition subtraction
9. ANS: q = 205 q = 205 Since q is divided by 5, multiply both sides by 5 to undo the division. Check: To check your solution, substitute 205 for q in the original equation. PTS: 1 DIF: 1 REF: 0f92325a-4683-11df-9c7d-001185f0d2ea OBJ: 1-3.1 Solving Equations by Using Multiplication NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.006 TOP: 1-3 Solving Equations by Multiplying or Dividing KEY: equation multiplication solving 10. ANS: n = 14 3n = 42 Since n is multiplied by 3, divide both sides by 3 to undo the multiplication. Check: 3n = 42 To check your solution, substitute 14 for n in the original equation. PTS: 1 DIF: 1 REF: 0f92596a-4683-11df-9c7d-001185f0d2ea OBJ: 1-3.2 Solving Equations by Using Division NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.007 TOP: 1-3 Solving Equations by Multiplying or Dividing KEY: equation solving multiplication
11. ANS: The reciprocal of is. Since is multiplied by, multiply both sides by. PTS: 1 DIF: 1 REF: 0f9494b6-4683-11df-9c7d-001185f0d2ea OBJ: 1-3.3 Solving Equations That Contain Fractions NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.006 TOP: 1-3 Solving Equations by Multiplying or Dividing 12. ANS: a = 15 First x is multiplied by 2. Then 14 is added. Work backward: Subtract 14 from both sides. Since x is multiplied by 2, divide both sides by 2 to undo the multiplication. PTS: 1 DIF: 1 REF: 0f99596e-4683-11df-9c7d-001185f0d2ea OBJ: 3-1.1 Solving Two-Step Equations NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.005 MTH.C.10.06.02.01.007 MTH.C.10.06.02.01.008 TOP: 3-1 Solving Two-Step and Multi-Step Equations KEY: equation two-step multi-step 13. ANS: Since is subtracted from, add to both sides to undo the subtraction. Since f is divided by 45, multiply both sides by 45 to undo the division. Simplify. PTS: 1 DIF: 2 REF: 0f99807e-4683-11df-9c7d-001185f0d2ea OBJ: 3-1.2 Solving Two-Step Equations That Contain Fractions NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.004 MTH.C.10.06.02.01.006 MTH.C.10.06.02.01.008 TOP: 3-1 Solving Two-Step and Multi-Step Equations KEY: equation two-step multi-step
14. ANS: Use the Commutative Property of Addition. Combine like terms. Since 10 is added to 17a, subtract 10 from both sides to undo the addition. Since a is multiplied by 17, divide both sides by 17 to undo the multiplication. PTS: 1 DIF: 2 REF: 0f9bbbca-4683-11df-9c7d-001185f0d2ea OBJ: 3-1.3 Simplifying Before Solving Equations NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.005 MTH.C.10.06.02.01.007 MTH.C.10.06.02.01.008 TOP: 3-1 Solving Two-Step and Multi-Step Equations KEY: equation two-step multi-step 15. ANS: 13 After paying $24.95 for roller skates, the number of visits to the roller rink that Devon can afford is. PTS: 1 DIF: 2 REF: 0f9e1e26-4683-11df-9c7d-001185f0d2ea OBJ: 3-1.4 Problem-Solving Application LOC: MTH.C.10.06.02.01.008 TOP: 3-1 Solving Two-Step and Multi-Step Equations KEY: multi-step equation 16. ANS: 1.55 Substitute 3750 for p, 3000 for n, and 900 for e. Add 900 to both sides of the equation. Divide both sides by 3000. PTS: 1 DIF: 3 REF: 0fa08082-4683-11df-9c7d-001185f0d2ea NAT: NT.CCSS.MTH.10.9-12.A.CED.4 STA: MCC9-12.A.CED.4 LOC: MTH.C.10.07.18.002 TOP: 3-1 Solving Two-Step and Multi-Step Equations KEY: equation two-step multi-step DOK: DOK 3
17. ANS: To collect the variable terms on one side, subtract 50q from both sides. Since 81 is subtracted from 2q, add 81 to both sides to undo the subtraction. Since q is multiplied by 2, divide both sides by 2 to undo the multiplication. PTS: 1 DIF: 2 REF: 0fa2e2de-4683-11df-9c7d-001185f0d2ea OBJ: 3-2.1 Solving Equations with Variables on Both Sides NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.06.02.01.008 MTH.C.10.06.02.01.009 TOP: 3-2 Solving Equations with Variables on Both Sides KEY: equation two-step multi-step 18. ANS: n = 1 1 2 n = 1 1 2 Combine like terms. Add to undo the subtraction. Or subtract to undo the addition. Then, divide to undo the multiplication. PTS: 1 DIF: 2 REF: 0fa309ee-4683-11df-9c7d-001185f0d2ea OBJ: 3-2.2 Simplifying Each Side Before Solving Equations NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.05.02.02.018 MTH.C.10.06.02.01.009 TOP: 3-2 Solving Equations with Variables on Both Sides KEY: equation equivalent equation terms
19. ANS: 5 movies Let m represent the number of movies rented each month. Here are the costs for each company (in dollars). 7.5 + m = 2.5m To collect the variable terms on one side, subtract m from both sides. 7.5 m = 2.5m m 7.5 = 1.5 m Divide both sides by 1.5. = m 5 = m PTS: 1 DIF: 2 REF: 0fa7a796-4683-11df-9c7d-001185f0d2ea OBJ: 3-2.4 Application LOC: MTH.C.10.06.02.01.009 TOP: 3-2 Solving Equations with Variables on Both Sides KEY: equation solving variables on both sides 20. ANS: 25.5 mph Divide both sides by t. Substitute the known values. Simplify. Round to the nearest tenth. PTS: 1 DIF: 2 REF: 0faa09f2-4683-11df-9c7d-001185f0d2ea OBJ: 3-3.1 Application NAT: NT.CCSS.MTH.10.9-12.A.CED.4 STA: MCC9-12.A.CED.4 LOC: MTH.C.10.07.18.002 TOP: 3-3 Solving for a Variable KEY: solving for a variable rate speed distance 21. ANS: V = Ir Locate V in the equation. Since V is divided by I, multiply both sides by I to undo the division. PTS: 1 DIF: 1 REF: 0fac6c4e-4683-11df-9c7d-001185f0d2ea OBJ: 3-3.2 Solving Formulas for a Variable NAT: NT.CCSS.MTH.10.9-12.A.CED.4 STA: MCC9-12.A.CED.4 LOC: MTH.C.10.07.18.002 TOP: 3-3 Solving for a Variable KEY: literal equation solving variables
22. ANS: Add z to both sides. Divide both sides by 4. PTS: 1 DIF: 1 REF: 0fac935e-4683-11df-9c7d-001185f0d2ea OBJ: 3-3.3 Solving Literal Equations for a Variable STA: MCC9-12.A.CED.4 TOP: 3-3 Solving for a Variable KEY: literal equation solving for a variable 23. ANS: 0 100 200 300 400 500 600 700 800 9001000 n The variable n must be greater than or equal to 500 yards for a swimmer to make the team. The graph should include the number 500 (solid circle at 500) and all the numbers to the right of 500 on the number line. PTS: 1 DIF: 2 REF: 101318d2-4683-11df-9c7d-001185f0d2ea OBJ: 4-1.4 Application NAT: NT.CCSS.MTH.10.9-12.A.CED.1 STA: MCC9-12.A.CED.3 LOC: MTH.C.10.08.02.01.005 MTH.C.10.08.02.01.007 TOP: 4-1 Graphing and Writing Inequalities KEY: inequalities graph number line 24. ANS: ; 500 400 300 200 100 0 100 200 300 400 500 Sam has $450, but must save $180 of that for his camping trip. If s is the amount he can spend on music, then. s So,. s 500 400 300 200 100 0 100 200 300 400 500 PTS: 1 DIF: 3 REF: 1015541e-4683-11df-9c7d-001185f0d2ea NAT: NT.CCSS.MTH.10.9-12.A.CED.1 NT.CCSS.MTH.10.9-12.A.REI.3 STA: MCC9-12.A.CED.1 MCC9-12.A.CED.3 LOC: MTH.C.10.08.02.01.005 MTH.C.10.08.02.01.007 TOP: 4-1 Graphing and Writing Inequalities KEY: inequalities graph number line DOK: DOK 3
25. ANS: s 3 0 1 2 3 4 5 6 7 8 9 10 11 number already downloaded + additional songs weekly limit 8 + s 11 Subtract 8 from both sides to undo the addition. s 3 Since you can only download whole songs, graph the nonnegative integers less than or equal to 3. 0 1 2 3 4 5 6 7 8 9 10 11 PTS: 1 DIF: 2 REF: 1017dd8a-4683-11df-9c7d-001185f0d2ea OBJ: 4-2.2 Problem-Solving Application NAT: NT.CCSS.MTH.10.9-12.A.CED.1 NT.CCSS.MTH.10.9-12.A.REI.3 STA: MCC9-12.N.Q.1 LOC: MTH.C.10.08.02.01.005 MTH.C.10.08.02.01.007 TOP: 4-2 Solving Inequalities by Adding or Subtracting KEY: solving inequality word problem 26. ANS: ; Let d represent the amount of money in dollars Denise must save to reach her goal. $365 plus additional amount of money is at least $635 in dollars 365 + d 635 365 365 Since 365 is added to d, subtract 365 from both sides to undo the addition. Check the endpoint 270 and a number that is greater than the endpoint. PTS: 1 DIF: 2 REF: 101a18d6-4683-11df-9c7d-001185f0d2ea OBJ: 4-2.3 Application NAT: NT.CCSS.MTH.10.9-12.A.CED.1 NT.CCSS.MTH.10.9-12.A.REI.3 STA: MCC9-12.A.CED.1 MCC9-12.N.Q.1 LOC: MTH.C.10.08.02.01.01.003 TOP: 4-2 Solving Inequalities by Adding or Subtracting KEY: inequalities solving adding subtracting
27. ANS: 5 tickets Divide both sides by the ticket price. The inequality symbol does not change. Simplify. 5 is the largest whole number less than 5.9. PTS: 1 DIF: 2 REF: 1023a246-4683-11df-9c7d-001185f0d2ea OBJ: 4-3.3 Application LOC: MTH.C.10.08.02.01.01.005 TOP: 4-3 Solving Inequalities by Multiplying or Dividing KEY: inequalities solving multiplying dividing 28. ANS: z 3 10 8 6 4 z + 8 3z 4 4z + 8 4 4z 12 z 3 2 0 2 4 6 8 10 Combine like terms. Subtract 8 from both sides. Divide both sides by 4. When you divide by a negative number, reverse the inequality symbol. When you divide by a positive number, keep the same inequality symbol. 10 8 6 4 2 0 2 4 6 8 10 Use a solid circle when the value is included in the graph, such as with or Use an empty circle when the value is not included, such as with > or <. PTS: 1 DIF: 2 REF: 102866fe-4683-11df-9c7d-001185f0d2ea OBJ: 5-1.2 Simplifying Before Solving Inequalities NAT: NT.CCSS.MTH.10.9-12.A.REI.3 LOC: MTH.C.10.08.02.01.01.007 MTH.C.10.08.02.01.005 TOP: 5-1 Solving Two-Step and Multi-Step Inequalities KEY: multistep inequality solving
29. ANS: 200 mi Let d represent the distance the family drove on the third day. The average number of miles is the sum of the miles of each day divided by 3. ( 150 plus 190 plus d ) divided 3 is at 180 by least ( 150 + 190 + d ) 3 180 Since is divided by 3, multiply both sides by 3 to undo the division. Combine like terms. Since 340 is added to d, subtract 340 from both sides to undo the addition. The least number of miles the family drove on the third day is 200. PTS: 1 DIF: 2 REF: 102ac95a-4683-11df-9c7d-001185f0d2ea OBJ: 5-1.3 Application LOC: MTH.C.10.08.02.01.01.007 TOP: 5-1 Solving Two-Step and Multi-Step Inequalities KEY: inequalities two-step multi-step DOK: DOK 3 30. ANS: More than 45 students Science plus $3 per student is less $12 per student Center fee than $135 + $3 s < $6 s 135 + 3s < 6s 3s 3s 135 < 3s < 45 < s If 45 < s, then s > 45. The Science Center charges less if there are more than 45 students. PTS: 1 DIF: 2 REF: 102d2bb6-4683-11df-9c7d-001185f0d2ea OBJ: 5-2.2 Application MCC9-12.A.CED.1 LOC: MTH.C.10.08.02.01.01.007 TOP: 5-2 Solving Inequalities with Variables on Both Sides KEY: multistep inequality solving word problem DOK: DOK 3
31. ANS: 250 200 150 100 50 0 50 100 150 200 250 Let n represent the possible number of people in the flight. 100 is less than or equal to n is less than or equal to 240 100 n 240 250 200 150 100 50 0 50 100 150 200 250 PTS: 1 DIF: 2 REF: 103452ca-4683-11df-9c7d-001185f0d2ea OBJ: 5-3.1 Application NAT: NT.CCSS.MTH.10.9-12.A.CED.1 STA: MCC9-12.A.CED.1 LOC: MTH.C.10.08.02.01.006 MTH.C.10.08.02.01.008 TOP: 5-3 Solving Compound Inequalities KEY: inequalities compound 32. ANS: yes Substitute 5 for x and 3 for y in both equations. Since these values make both equations true, (5, 3) is a solution of the system. PTS: 1 DIF: 1 REF: 1120836e-4683-11df-9c7d-001185f0d2ea OBJ: 6-1.1 Identifying Solutions of Systems NAT: NT.CCSS.MTH.10.9-12.A.REI.6 NT.CCSS.MTH.10.9-12.A.REI.11 STA: MCC9-12.A.REI.6 MCC9-12.A.REI.11 LOC: MTH.C.10.09.01.01.01.005 TOP: 6-1 Solving Systems by Graphing KEY: ordered pair system of equations solution
33. ANS: y 10 8 6 4 2 10 8 6 4 2 2 4 6 8 10 x 2 4 6 8 10 Write each equation in slope-intercept form,. Plot the y-intercept (0, b), and use the slope (m) to find a second point on the line. Draw the second line in the same way. Find the coordinates of the point where the lines intersect. This is the solution. PTS: 1 DIF: 2 REF: 1122beba-4683-11df-9c7d-001185f0d2ea OBJ: 6-1.2 Solving a System of Linear Equations by Graphing NAT: NT.CCSS.MTH.10.9-12.A.REI.6 NT.CCSS.MTH.10.9-12.A.REI.11 STA: MCC9-12.A.REI.6 MCC9-12.A.REI.11 LOC: MTH.C.10.09.01.01.01.005 TOP: 6-1 Solving Systems by Graphing KEY: coordinate plane graphing solving system of equations
34. ANS: 4 games; $27 Write a system of equations. Total cost is cost per game plus annual fee Fun Guys y = 5.5 + 5 Game Bank y = 2.5 + 17 Graph the two equations. 100 y 90 80 70 60 50 40 30 20 10 3 6 9 12 15 18 21 x The lines appear to intersect at (4, 27). So the cost will be the same after 4 games, and that cost will be $27. PTS: 1 DIF: 2 REF: 11252116-4683-11df-9c7d-001185f0d2ea OBJ: 6-1.3 Problem-Solving Application STA: MCC9-12.A.REI.6 MCC9-12.A.REI.11 LOC: MTH.C.10.09.01.01.01.004 TOP: 6-1 Solving Systems by Graphing KEY: systems of linear equations solving systems of linear equations two unknowns 35. ANS: Month 11; 550 Continue the pattern. Subtract 15 from the number of CDs and add 45 to the number of movie tickets. In month 11, both the number of CDs and the number of movie tickets will be 550. PTS: 1 DIF: 3 REF: 11254826-4683-11df-9c7d-001185f0d2ea STA: MCC9-12.A.REI.6 MCC9-12.A.REI.11 LOC: MTH.C.10.09.01.01.01.002 MTH.C.10.09.01.01.01.003 TOP: 6-1 Solving Systems by Graphing KEY: pattern arithmetic DOK: DOK 3
36. ANS: ( 2, 3) Step 1 The second equation is solved for y. Step 2 Substitute for y in the first equation. Step 3 Simplify and solve for x. x = 2 Divide both sides by 4. Step 4 Write one of the original equations. y = 2 Substitute 2 for x. 3 Find the value of y. ( 2, 3) Write the solution as an ordered pair. PTS: 1 DIF: 1 REF: 11278372-4683-11df-9c7d-001185f0d2ea OBJ: 6-2.1 Solving a System of Linear Equations by Substitution NAT: NT.CCSS.MTH.10.9-12.A.REI.6 STA: MCC9-12.A.REI.6 LOC: MTH.C.10.09.01.01.01.001 TOP: 6-2 Solving Systems by Substitution KEY: system of equations substitution 37. ANS: (4, 8) Step 1 x = 2y 12 Solve the second equation for x. Step 2 4(2y 12) 4y = 16 Substitute 2y 12 for x in the first equation. Step 3 8y 48 4y = 16 Use the Distributive Property to simplify. 4y 48 = 16 Collect like terms. 4y = 16 ( 48) 4y = 32 Subtract 48 from both sides. Divide both sides by 4. y = 8 Step 4 x 2y = 12 x 2(8) = 12 x 16 = 12 x = 12 ( 16) x = 4 Write one of the original equations. Substitute 8 for y. Subtract 16 from both sides. Step 5 (4, 8) Write the solution as an ordered pair. PTS: 1 DIF: 2 REF: 1129e5ce-4683-11df-9c7d-001185f0d2ea OBJ: 6-2.2 Using the Distributive Property NAT: NT.CCSS.MTH.10.9-12.A.REI.6 STA: MCC9-12.A.REI.6 LOC: MTH.C.10.02.03.002 MTH.C.10.09.01.01.01.001
TOP: 6-2 Solving Systems by Substitution KEY: system of equations substitution 38. ANS: The Pup Palace Kennel is cheaper than Nguyen s Kennel after 5 days. Let t represent the total amount paid and let d represent the number of days. Nguyen s Kennel: Pup Palace: Substitute for t in the second equation and solve for w. The costs for the two kennels are equal at 5 days. After that, the Pup Palace Kennel is cheaper. PTS: 1 DIF: 2 REF: 112a0cde-4683-11df-9c7d-001185f0d2ea OBJ: 6-2.3 Application STA: MCC9-12.A.REI.6 LOC: MTH.C.10.09.01.01.01.001 TOP: 6-2 Solving Systems by Substitution KEY: system of equations substitution 39. ANS: (4, 1) Step 1 2x 3y = 11 3x + 3y = 9 The y-terms have opposite coefficients. 5x = 20 Add the equations to eliminate the y terms. x = 4 Step 2 2(4) 3y = 11 Substitute for x in one of the original equations. 8 3y = 11 Simplify and solve for y. 3y = 3 y = 1 (4, 1) Write the solution as an ordered pair. PTS: 1 DIF: 1 REF: 112eaa86-4683-11df-9c7d-001185f0d2ea OBJ: 6-3.1 Elimination Using Addition NAT: NT.CCSS.MTH.10.9-12.A.REI.6 STA: MCC9-12.A.REI.6 LOC: MTH.C.10.09.01.01.01.002 TOP: 6-3 Solving Systems by Elimination KEY: linear equation system of equations solving elimination
40. ANS: ( 5, 8) Multiply all expressions in the second equation by. Add the two equations together. Divide both sides by 2. Solve for x. Substitute the value for x into one of the original equations and solve for y. PTS: 1 DIF: 2 REF: 112ed196-4683-11df-9c7d-001185f0d2ea OBJ: 6-3.2 Elimination Using Subtraction NAT: NT.CCSS.MTH.10.9-12.A.REI.6 STA: MCC9-12.A.REI.6 LOC: MTH.C.10.09.01.01.01.003 TOP: 6-3 Solving Systems by Elimination KEY: system of equations elimination 41. ANS: (4, 3) First, multiply each equation by a number to get opposite coefficients. Multiply the first equation by 3 and the second by 5 to get opposite y-coefficients. Step 1 Add the two equations to eliminate the y-term. Step 2 Simplify and solve for x. x = 4 Step 3 Write one of the original equations. Substitute 4 for x. Simplify and solve for y. y = 3 PTS: 1 DIF: 2 REF: 11310ce2-4683-11df-9c7d-001185f0d2ea OBJ: 6-3.3 Elimination Using Multiplication First NAT: NT.CCSS.MTH.10.9-12.A.REI.6 STA: MCC9-12.A.REI.6 TOP: 6-3 Solving Systems by Elimination KEY: system of equations elimination
42. ANS: 7 zebra fish, 6 neon tetras Let z be the number of zebra fish and let n be the number of neon tetras that Marsha bought. Then solve the following system of equations. Marsha spent $25.80. Marsha bought 13 fish. Multiply the second equation by 2.10 Add the two equations to eliminate the z term. Solve for n. To solve for z, substitute 6 for n in the first equation. Simplify. Solve for z. PTS: 1 DIF: 2 REF: 11336f3e-4683-11df-9c7d-001185f0d2ea OBJ: 6-3.4 Application STA: MCC9-12.A.REI.6 TOP: 6-3 Solving Systems by Elimination KEY: system of equations elimination