Direct Variation Word Problems

1. Direct Variation Word Problems Chapter 5.2

2. Direct Variation Word Problems • Lesson Objective: NCSCOS 4.01 – Students will know how to solve problems using direct variation

3. Direct Variation Word Problems • The amount of a person’s paycheck varies directly with the number of hours worked. For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. • “varies directly” means: • Remember, “y” always varies directly as “x” y = kx

4. Direct Variation Word Problems • The amount of a person’s varies directly with the number of For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. • If “y” varies directly as “x” than what comes before varies directly is y and what comes after it is x paycheck hours worked.

5. Direct Variation Word Problems • Remember, varies directly with 3 numbers means: • In this problem it means: y y = x x Paycheck hours

6. Direct Variation Word Problems • The amount of a person’s paycheck varies directly with the number of hours worked. For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. • Replace paycheck with $73.45 and hours with 13 and then 25 for hours in the second fraction Paycheck Paycheck = hours hours

7. Direct Variation Word Problems • The amount of a person’s paycheck varies directly with the number of hours worked. For 13 hours of work, the paycheck is $73.45. Find the pay for 25 hours of work. • Replace paycheck with $73.45 and hours with 13 and then 25 for hours in the second fraction 73.45 Paycheck = 13 25

8. Direct Variation Word Problems • Cross Multiply • Solve the equation 73.45 P = 13 25 13p = 1836.25 13 13 p = 141.25

9. Direct Variation Word Problems • The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in a 15-ounce glass of milk. • Directly proportional means direct variation y = kx

10. Direct Variation Word Problems • The number of calories in a container of milk is directly proportional to the amount of milk in the container. • Y varies directly as x, so calories is y and amount of milk is x calories milk

11. Direct Variation Word Problems • The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in a 15-ounce glass of milk. calories calories = milk milk

12. Direct Variation Word Problems • The number of calories in a container of milk is directly proportional to the amount of milk in the container. If there are 160 calories in an 8-ounce glass of milk, find the number of calories in a 15-ounce glass of milk. 160 calories = 8 15

13. Direct Variation Word Problems • Cross Multiply • Solve the equation 160 c = 8 15 8c = 2400 8 8 c = 300

14. Direct Variation Word Problems • Laura typed 176 words correctly in 4 minutes. Assuming a direct variation, how many words can she type in 30 minutes? • A refund you get varies directly as the number of cans you recycle. If you get a $3.75 refund for 75 cans, how much should you get for 500 cans?

15. Direct Variation Word Problems • The number of miles driven varies directly with the number of gallons of gas used. Erin drove 297 miles on 9 gallons of gas. How far would she be able to drive on 14 gallons of gas? • The kinetic energy of a car varies directly with the square of the velocity of the car. A car with a velocity of 9 meters per second has 33,100 joules of kinetic energy. About how much kinetic energy does the same car have when traveling at 12 meters per second?

16. Direct Variation Word Problems • The height of a kite from the ground varies directly with the cube of the wind speed. A kite flies 8 feet high when the wind speed is 10 miles per hour. What is the height of a kite when the wind speed is 25 miles per hour?