2009 AMC 10A Problem 8

Question

Three generations of the Wen family are going to the movies, two from each generation. The two members of the youngest generation receive a

50\%

discount as children. The two members of the oldest generation receive a

25\%

discount as senior citizens. The two members of the middle generation receive no discount. Grandfather Wen, whose senior ticket costs

\$6.00,

is paying for everyone. How many dollars must he pay?

34

36

42

46

48

A senior ticket is

75\%

of the full price, so find the full price first

Add two senior, two full, and two child tickets

The senior ticket costs

\$6,

which is

\dfrac34

of the full price, so a full ticket costs

\dfrac43 \cdot 6 = \$8,

and a child ticket costs

\dfrac12 \cdot 8 = \$4.

The total is

2(6 + 8 + 4) = \$36.

Thus, the correct answer is B.

Problem 8 in other years