Math Models Unit 1 Lesson 9

12. Use proportions to solve the problem. The cost of carpeting a floor varies directly with the size of the floor. If a 400 square foot floor costs $1,800, what is the cost of flooring for a 625 square foot floor? (Hint: The cost per square foot would be the constant of proportionality.)

$2,812.50

4. Find the constant of proportionality. -15 = k(15)

-1

8. Given the constant of proportionality and the value of one of the variables, find the value of the other variable. y = kx k = -4 x = 5/6 Find the value of y.

-20/6

9. Given the constant of proportionality and the value of one of the variables, find the value of the other variable. y = kx k = 2 y = -3 Find the value of x.

-3/2

6. Given the constant of proportionality and the value of one of the variables, find the value of the other variable. y = kx k = 2 x = -3 Find the value of y.

-6

5. Find the constant of proportionality. -12 = k( - 36)

1/3

3. Find the constant of proportionality. 27.5 = k(2.75)

10

7. Given the constant of proportionality and the value of one of the variables, find the value of the other variable. y = kx k = 2/3 x = 5 Find the value of y.

10/3

10. Given the constant of proportionality and the value of one of the variables, find the value of the other variable. y = kx k = 3/5 y = 2/3 Find the value of x.

10/9

11. Use proportions to solve the problem. The weight of a snake is directly proportional to its length. If a 4 foot snake weighs 2.5 lbs, how much would a 5 foot snake weigh?

3.125 Ibs

15. Use proportions to solve the problem. The state is considering building an HOV (High Occupancy Vehicle) lane for a new highway. Of the 50,000 cars going from Fort Worth to Dallas in a day, 32,000 had only one occupant while the other 18,000 had the necessary two or more occupants to use an HOV lane. What percentage of the cars observed would qualify to use the HOV lane? (Hint: The constant of proportionality between the number of cars qualified to use the HOV lane and the total number of cars would be the percentage.)

36%

1. Find the constant of proportionality. 115 = k(25)

4.6

2. Find the constant of proportionality. 15 = k(2.5)

6

14. Use proportions to solve the problem. The distance an object travels in uniform motion varies directly with the time it travels. In the first second of travel, an object travels 16 meters. How long will it take the object to travel a distance of 1,101 meters? (Hint: The constant of proportionality would be the speed of the object.)

68.8125 seconds

13. Use proportions to solve the problem. The ratio of cars to pickup trucks sold at a dealership is 2 to 3. If the dealer sold 114 pickup trucks last month, how many cars were sold?

76