Question

At the city museum, child admission is $5.90 and adult admission is $9.70. On Tuesday, three times as many adult tickets as child tickets were sold, for a total
sales of $1085.00. How many child tickets were sold that day?
Could someone explain to me how to do this?

Answer 1

Answer:

$\large \boxed{31}$

Step-by-step explanation:

1. Set up the equations

              Let a = the number of adult tickets

             and c = the number of child tickets. Then

             9.70a = revenue from adult tickets and

             5.90c = revenue from child tickets

9.70 a + 5.90c = total ticket revenue

You have a system of two equations:

$\begin{cases}(1) & a = 3c\\(2) & 9.70a + 5.90c = 1085\end{cases}$

2. Solve the equations

$\begin{array}{lrcll}(3) & 9.70(3c) + 5.90c & = & 1085 &\text{Substituted (1) into (2)}\\& 29.10c + 5.90c & = & 1085 &\text{Simplified}\\& 35c & = & 1085 &\text{Simplified}\\& c & = & \dfrac{1085}{35} &\text{Divided each side by 35}\\\\(4) && = & \mathbf{31} &\text{Simplified}\\\end{array}\\\text{The museum sold \large \boxed{\textbf{31 child tickets}} }$