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Algebra 2C Name__________________________

Direct and Inverse Variation Practice

Write an equation for each statement. Use “k” as your variation constant.

1. t varies directly with u.

2. q is directly proportional to p.

3. r varies inversely as w.

4. t in inversely proportional to r.

5. Look at each table and decide whether it shows direct variation, inverse variation or neither. If it shows direct or inverse, write an equation.

|X |Y |

|2 |10 |

|10 |20 |

|12 |24 |

|X |Y |

|-12 |4 |

|-3 |1 |

|15 |-5 |

6. y varies inversely with x. When x = 8, y = 4. Find y when x = 2

7. y is directly proportional to x. When x = 8, y = 4. Find y when x = 2

8. t is inversely proportional to r. When t = 2, r = 9. Find r when t = 6.

9. t varies directly as r. When t = 2, r = 9. Find r when t = 6.

10. There are about 220 calories in 40 grams of Bleu cheese. Nathan ate 60 grams of this cheese.  About how many calories were in the cheese that he ate if the number of calories varies directly as the mass of the cheese?

11. The volume V of a gas varies inversely as the pressure P upon it. If the volume of a gas is 250 cm3 under a pressure of 40 kg/cm2, what will be its volume under a pressure of 50 kg/cm2?

12. The resistance (R) of a copper wire, varies directly as its length (L).  When the resistance is 80, the length is 10 inches. What is the resistance when the length is 15 inches?

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|13. |

|Given a triangle with a fixed area, the base b varies inversely as the height h. If the initial height of the triangle is 7 cm and the base is 18 |

|cm, then what is the length of the base of the triangle if the height is changed to 14 cm? |

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|14.  |

|Given a rectangle with a fixed area, the length l varies inversely as the width w. If the length of the rectangle is 5 in and the width is 12 in, |

|then what is the length if the width is 10 in? |

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|15.  |

|The time t required to do a job varies inversely as the number of people P who work on the job. If it takes 49 hours for 4 carpenters to build 8 dining|

|room sets, how long would it take for 28 carpenters to complete the same job? |

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|X |Y |

|1 |2 |

|2 |5 |

|3 |8 |

|4 |11 |

|X |Y |

|-0.5 |-8 |

|1 |4 |

|2 |2 |

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