Question

John charges a flat fixed fee of $10 PLUS a certain rate per hour for each hour for cutting the grass. John earned $100 one day, cutting the grass in a circular lawn. On the next day, to cut the grass in a similar adjacent circular lawn one third the circumference, how much money can he expect to make? ( with explanation )

Answer 1

33.33 dollars

Explanation:

Answer 2

$20

Explanation:

Of the $100 John earned, $90 was for his hourly charge, which we assume is proportional to the area being mowed.

A lawn with 1/3 the circumference has (1/3)^2 = 1/9 the area, so presumably takes 1/9 of the time to mow. John's hourly charge for the smaller lawn will be $90/9 = $10. Added to his flat fee, he can expect to be paid $20.

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The ratio of areas of similar figures is the square of the ratio of any of the linear dimensions. All circles are similar. Circumference is measured in "units" and area is measured in "square units." So, circumference is a linear dimension (units to the first power).