1996 AMC 12 Problem 7

Question

A father takes his twins and a younger child out to dinner on the twins’ birthday. The restaurant charges

\$4.95

for the father and

\$0.45

for each year of a child’s age, where age is defined as the age at the most recent birthday. If the bill is

\$9.45,

which of the following could be the age of the youngest child?

1

2

3

4

5

Subtract the father’s charge and divide the remainder by the price per year

If the twins are

t

years old and the younger child is

y

, impose both

2t+y=10

and

y\lt t

The children account for

9.45-4.95=4.50

dollars, so their ages total

\frac{4.50}{0.45}=10.

If each twin is

t

and the younger child is

y,

then

2t+y=10

with

y\lt t.

Of the choices,

y=2

gives

t=4,

which works. Thus the correct answer is B.

Problem 7 in other years