Variations Review Honors

There are about 200 calories in 50 grams of Swiss cheese. James ate 70 grams of this cheese. About how many calories were in the cheese that he ate if the calories varies directly as the weight?

• 210

• 240

• 280

• 290

The time, t, in hours, that it takes x people to plant n trees varies directly with the number of trees and inversely with the number of people. Suppose 6 people can plant 12 trees in 3 hours. How many people are needed to plant 28 trees in 5 hours and 15 minutes?

• 6

• 7

• 8

• 9

The time to prepare a field for planting is inversely proportional to the number of people who are working. A large field can be prepared by 6 workers in 30 days. In order to finish earlier, the farmer must hire more workers. How many workers are needed to finish the field in 10 days

• 10

• 12

• 18

• 7

A recipe for 2 dozen cupcakes uses 5 cups of flour. The number of cupcakes varies directly with the amount of flour that you use? Write the direct variation equation to represent this relationship and estimate how many cups of flour are needed to make 8 dozen muffins?

• c= 5/2f, 16/2 cups

• c= 2/3 f, 9 cups

• c= 2/5 f, 20 cups

• c= 20f, 2/5 cups

The number of people at a dinner party is inversely related to the cost that each person will have to pay to attend the dinner. If there are 15 people attending then each person will have to pay $12. How much will a person have to pay if there are 25 people attending ?

• $1

• $6.67

• $7.20

• $9

A contractor decides that he can build a barn in 8 weeks using 4 men. If he employs 4 more men, how long will the job take assuming the men all work at the same rate?

• 4

• 8

• 5

• 40

Solve for x :

3x - 7 < 5x + 9

• x < 2

• x > 2

• x < -8

• x > -8

The number of kilograms of water in a person's body varies directly as the person's mass. A person with a mass of 90kg contains 60kg of water. What is the mass of a person who contains 80kg of water?

• 80

• 120

• 150

• 180

For rectangles with the same area, the length varies inversely as the width. One rectangle has a length of 10cm and a width of 6cm. Find the length of another rectangle with the same area whose width is 5cm?

• 15

• 12

• 10

• 8

The distance, d , through which a stone falls from rest varies directly as the square of the time taken, t. If the stone falls 80m in 4 seconds , how far will it fall in 11 seconds?

• 55m

• 220m

• 5m

• 605m