Question

Write and solve a system of equations for each problem

Answer 1

The price of one adult ticket was $52

Step-by-step 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*3 \\ 2a+3c=239---ii*1 \\ 9a+3c=603---iii \\ 2a+3c=239---ii \\ (iii)-(ii) \\ 9a-2a+3c-3c=603-239 \\ 7a=364 \\ \text{Divide both sides by 7} \\ (7a)/(7)=(364)/(7) \\ a=52 \end{gathered}`

Therefore, the price of one adult ticket was $52