# A group consisting of several families visited an amusement park where…

## Solution:

We are given that at an amusement park, regular admission fees were ¥5,500 for each adult and ¥4,800 for each child. However, a particular group paid 10% less than the regular admission fee. Thus, the admission fee per adult was 5,500 x 0.9 = 4,950 yen and per child was 4,800 x 0.9 = 4,320 yen. We need to determine the number of children in the group.

Statement One Alone:

The total of the admission fees paid for the adults in the group was ¥29,700.

If we let the number of adults = A, we can create the following equation:

4,950A = 29,700

A = 6

However, since we do not know the number of children, statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The total of the admission fees paid for the children in the group was ¥4,860 more than the total of the admission fees paid for the adults in the group.

If we let C = the number of children, we can create the following equation:

4,320C = 4,860 + 4,950A

We see that we do not have enough information to determine C. We can eliminate answer choice B.

Statements One and Two Together:

Using the information from statements one and two, we know that A = 6 and 4,320C = 4,860 + 4,950A. We can see that if we substitute 6 for A in 4,320C = 4,860 + 4,950A, we can determine the value of C. The two statements together are sufficient.