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Proportional relationships

Find the constant of variation: word problems

The weight of an object on Earth varies directly as its weight on the moon. If an rock weighed 5 pounds on the moon and 30 pounds on Earth and another rock weighted 26 pounds on the moon and 156 pounds on Earth, what is the constant of variation?

Create a chart.

 Weight (on the moon) 5 26 Weight (on Earth) 30 156

To find the constant of variation, divide "weight on Earth" by "weight on the moon".

 Weight (on the moon), x 5 26 Weight (on Earth), y 30 156 Constant of variation, y/x 6 6

The constant of variation is 6.

The cost of a bus ticket varies directly with the number of miles travelled. If a ticket for a 180-mile trip cost $45, and a ticket for a 1,500-mile trip cost$375, what is the constant of variation?

Create a chart.

 distance (miles) 180 1,500 price ($) 45 375 To find the constant of variation, divide "price" by "distance".  distance (miles), x 180 1,500 price ($), y 45 375 Constant of variation, y/x 0.25 0.25

The constant of variation is 0.25.