Question

Two families went to the Zoo. The Diaz family paid $170 for 3 children and 2 adults. The Jones family paid $360 for 4 children and 6 adults. If x is the price of a child’s ticket and y is the price of an adult’s ticket in dollars.

A. write a system of equations that models this situation.
B. How much does a child’s ticket cost?

Answer 1

`\mathrm{A.\:}\begin{cases}3x+2y=170,\\4x+6y=360\end{cases}\\\\\mathrm{B.\:} \$ 30`

Explanation:

We can write the following system of equations:

`\begin{cases}3x+2y=170,\\4x+6y=360\end{cases}`, with variables as defined in the question.

Multiply the first equation by
`-3` and add both equations to isolate and solve for
`x`:

`\begin{cases}-9x-6y=-510,\\4x+6y=360\end{cases}\\-5x=-150,\\x=\fbox{$\$ 30$}`.