Chapter 11, Problem 42CLR

To determine

To find: The admission price for children and adult.

Answer to Problem 42CLR

The admission price for children is $\$2.5$ and the admission price for adult is $\$60$ .

Explanation of Solution

Given information:

The group one consists of ten adults and for children, group two consists five adults and sixteen children and the amount paid by each group is $\$70$ .

Calculation:

Assume price of admission for adults is $x$ and the amount for admission of children is $y$ .

Form the linear equation using given information.

  $10x+4y=70$ ..... (1)

  $5x+16y=70$ ..... (2)

Rearrange equation (2).

  $x=\frac{70-16y}{5}$

Substitute the value of $x$ in equation (1).

  $\begin{array}{c}10\left(\frac{70-16y}{5}\right)+4y=70\\ -32y+4y=70-140\\ -28y=-70\\ y=\$2.5\end{array}$

Substitute the value of $y$ in equation (1).

  $\begin{array}{c}10x+4\left(2.5\right)=70\\ 10x=70-10\\ x=\$60\end{array}$

Therefore, the admission price for children is $\$2.5$ and the admission price for adult is $\$60$