can be used to represent this situation.

Transcription

1 Question 1. Solve the real-world situation by using the substitution method. A cable television provider has a $70 setup fee and charges $82 per month, while a satellite television provider has a $175 setup fee and charges $67 per month. Let c represent the total cost in dollars and t represent the amount of time in months. The system of equations c = t c = t can be used to represent this situation. Part 1 In how many months will both providers cost the same? What will that cost be? Both providers will cost $ in months. Part 2 If you plan to move in 12 months, which provider would be less expensive? Complete the explanation. (select) would be less expensive because it costs less per month than the other provider and 12 months is after 7 months. 1/12

2 Question 2. Drag and drop each system of equations into the correct category to show whether each of the following systems have one solution, infinitely many solutions, or no solution. 2x + 5y = 23 x + 7y = 34 x + y = 10 5x + 2y = 29 3x + y = 12 6x + 2y = 26 3x + 5y = 22 6x 10y = 44 x + y = 12 6x 6y = 12 One Solution Infinitely Many Solutions No Solution 2/12

3 Question 3. Adrienne invested a total of $ in two simple-interest money market accounts. Account A paid 3% annual interest and account B paid 5% annual interest. The total amount of interest she earned after one year was $ If a represents the amount invested in dollars in account A and b represents the amount invested in dollars in account B, the system of equations a + b = can be used to represent this situation. 0.03a b = How much did Adrienne invest in each account? Adrienne invested $ in account A and $ in account B. 3/12

4 Question 4. Max and Sasha exercise a total of 20 hours each week. Max exercises 10 hours less than 4 times the number of hours Sasha exercises. The system of equations shown below represents this situation, where x represents the number of hours Max exercises and y represents the number of hours Sasha exercises. How many hours do Max and Sasha exercise per week? x + y = 20 x 4y = 10 Max exercises hours a week and Sasha exercises hours a week. 4/12

5 Question 5. The sum of the digits in a two-digit number is 14. The digit in the tens place is 2 more than the digit in the ones place. The system of linear equations shown below represents this situation, where x is the digit in the tens place and y is the digit in the ones place. Solve the system to find the two-digit number. x + y = 14 x y = 2 The two digit number is. 5/12

6 Question 6. A pool company is installing a rectangular pool for a new house. The perimeter of the pool must be 82 feet, and the length must be 2 feet more than twice the width. The system of linear equations shown below represents this situation, where l is the length and w is the width. What are the dimensions of the pool? 2l + 2w = 82 l = 2w + 2 The length of the pool is feet and the width is feet. 6/12

7 Question 7. Solve the problem by multiplying first. Jayce bought 5 bath towels and returned 2 hand towels. His sister Jayna bought 3 bath towels and returned 4 hand towels. Jayce paid a total of $123 and Jayna paid a total of $43. The system of equations 5b 2h = 123 3b 4h = 43 models this situation, where b is the price of a bath towel and h is the price of a hand towel. How much does each kind of towel cost? Bath towels cost $ each and hand towels cost $ each. 7/12

8 Question 8. Solve the problem by multiplying first. Apples cost $0.90 per pound and bananas cost $1.10 per pound. Leah bought a total of 13 pounds of apples and bananas for $ The system of equations a + b = a b = models this situation, where a is the number of pounds of apples and b is the number of pounds of bananas. How many pounds of each did Leah buy? Leah bought pounds of apples and pounds of bananas. 8/12

9 Question 9. Part 1 Select the graph of the system of linear inequalities. y 2x + 5 y < 1 2 x 1 Part 2 Select the ordered pairs which are solutions to the system. ( 6, 6) ( 8, 6) (8, 6) (0, 0) 9/12

10 Question 10. Part 1 Select the graph of the system of linear inequalities. y 4 5 x 3 y < 2x 4 Part 2 Select the ordered pairs which are solutions to the system. (1, 7) (3, 7) (5, 5) ( 3, 1) 10/12

11 Question 11. Select the graph of the system of linear inequalities. y 9 4 x 4 y < 9 4 x 8 Select the correct description of the solutions. A. The solutions are the same as the B. solutions of y < 9 4 x 8. The solutions are all real numbers. This system has no solution. The solutions are the same as the solutions of y 9 4 x /12

12 Question 12. Select the graph of the system of linear inequalities. y < 3 5 x + 2 y 3 5 x 5 Select the correct description of the solutions. The solutions are all points between the parallel lines and on the solid line. C. The solutions are the same as the D. solutions of y 3 5 x 5. This system has no solution. The solutions are the same as the solutions of y < 3 5 x /12