Question

Write and solve a system of equations for each problem

Answer 1

Answer

The price of one adult ticket was $52

Explanation

Let a represent an adult ticket and c represent a child ticket.

For the Smith family, we have the relation below

$3a+c=201\text{ -----}i$

And for the Brown family, the relation is

$2a+3c=239\text{ ------}ii$

Now, compare (i) and (ii)

$\begin{gathered} 3a+c=201----i \\ 2a+3c=239---ii \end{gathered}$

To get a, use elimination method of simultaneous equation

$\begin{gathered} 3a+c=201----i\times3 \\ 2a+3c=239---ii\times1 \\ 9a+3c=603---iii \\ 2a+3c=239---ii \\ (iii)-(ii) \\ 9a-2a+3c-3c=603-239 \\ 7a=364 \\ \text{Divide both sides by 7} \\ \frac{7a}{7}=\frac{364}{7} \\ a=52 \end{gathered}$

Therefore, the price of one adult ticket was $52