PROJECT - Systems of Equations and Matrix Equations

Transcription

1 PROJECT - Systems of Equations and Matrix Equations NAME AND CLASS PERIOD Due on: If turned in by _ by 4:15, you may earn 5 extra points. To earn 5 more extra points, make up your own WORD PROBLEM for a 3 equation system. Then write the equations & solve the system using matrices! *1. Write the formula for perimeter of a rectangle. given So, 85 =, factoring we get This eliminates answers and L = That eliminates answers and What is left? When a problem is discussing shapes always draw a picture! w *2. Chase bought fudge and gum for $ Write it down as an equation: Sara bought fudge and gum for $3.60 Write it down as an equation: *3. Write two equations:

2 *4. l = LAST WEEK t = THIS WEEK Last week PLUS this week she sold CDS. SO l + t = This did not help Last week = 6 more than 3 times as many as this week. We need an equation that starts with l = Eliminate and Six more means addition or subtraction? Only one answer left has a +6. _ 5. Hector (h) and Martha (m) collected stamps, so Eliminate answers and. If Hector gives Martha 4 stamps, do you add or subtract them from Hector? Then do you add or subtract them to Martha? So Hector has stamps. (in terms of h, not a number) Martha will have 3 times as many as Hector. Which answer has 3 times and many as Hector. *6. How much are sundaes? How much are banana splits? Sundaes are represented by what letter? So, if we want to know how much was spent on sundaes we would write Banana splits are represented by what letter? So, if we want to know how much was spent on banana splits we would write The total price sundaes and banana splits sold was $ How many more sundaes were sold than banana splits? So, sundaes= banana splits +. Write this equation. Also, sundaes plus banana splits = $. Write this equation. What is the answer?

3 7. *8. *9. A food store makes a 13-lb mixture of peanuts, cashews, and raisins. Peanuts cost $1.00 per pound, cashews cost $3.00 per pound, and raisins cost $1.00 per pound. The mixture calls for twice as much peanuts than cashews. The total cost of the mixture is $ How much of each ingredient did the store use? Do not solve at this time. Write a system of equations: *10. Explain why.

4 11. The answer has to be 75 or 5. Why? _ But while we are here, what is the equation for the Garden club? Y = What is the equation for the local nursery? Y =

5 12. Write an equation for the total number of teachers: How would you write twice the number of men Then add 5 to that and you get *13. Tasty Bakery sells three kinds of muffins: chocolate chip muffins for $0.70 each, oatmeal muffins for $0.50 each, and blueberry muffins for $0.60 cents each. Charles buys some of each kind and chooses three more chocolate chip muffins than blueberry muffins. If he spends $11.10 on 18 muffins, how many of each type of muffin does he buy? Write a system of three equations in three variables.. ANSWER: *14. Write an equation for the cost of the text and the novel: _ That should eliminate answers and Write an equation for the cost of the math book:

6 15. We get three choices: What does difference mean? So which one can we eliminate? Is there any reason that the difference between two prices would be -175? Write an equation for the cost of e : e = What does this match the given equation in the answer?

7 PART 2: NOW WE ARE GOING TO SOLVE SOME OF THE SYSTEMS OF EQUATIONS THAT WERE PRESENTED IN THIS PACKET OF PROBLEMS. For the systems of 2 equations and 2 unknowns, choose the best method to solve: Elimination or substitution. Where instructed use matrix equations. Problem numbers refer to the problems in Part 1 1. Use Substitution or Elimination? Show all work 2. Solve by using a MATRIX EQUATION. Answer: Length =Width= Answer fudge gum 3. Use Substitution or Elimination? Show all work 4. Use Substitution or Elimination? Show all work Answer: Nickels Quarters Answer: last week This week:

8 6. Use Substitution or Elimination? Show all work 8. Solve by using a MATRIX EQUATION. Answer: =sundaes banana splits= Answer brownies= cookies= 9. Equation Three _ Solve using a MATRIX EQUATION. 10. Answer: peanuts cashews raisins Answer: x = y =

9 12. Solve using a MATRIX EQUATION. 14. Equation One _ Equation Two_ Solve using a MATRIX EQUATION. Answer: # men # women Answer: Cost of Math Book Cost of Novel