Question

The course fee per child of a summer camp varies inversely as the number of participating children. If there are 50 children participating in the camp, the course fee is $372 per child. Identify the course fee per child, if 75 children join the camp.

Answer 1

$248

Explanation:

Method 1 Find k and substitute into the variation function.

Find k.

y = k/x

372 = k/50 Substitute.

k = 18600 Solve for k.

Use the variation function.

y = 18600/x

y = 18600/75 Substitute.

y = 248 Solve for y.

Method 2

x1y1 = x2y2

50(372) = (75)y2 Substitute.

18600 = 75y2 Simplify.

y2 = 248 Solve for y2.

So, the course fee will be $248 per child if 75 children join the camp.

Answer 2

The cost per child = $248

Explanation:

∵ The cost per child ∝ 1/number of children

∴ C.C = K/N.C ⇒ (K is a constant)

∵ C.C = $372 , N.C = 50

∴ 372 = K/50

∴ K = 372 × 50 = 18600

∴ C.C = 18600/N.C

∵ N.C = 75

∴ C.C = 18600/75 = $248