Question

A minor league ballpark attracts $88$ fans and draws in $$553$ in revenue from ticket sales. A child's ticket costs $$4$ and an adult's ticket is $$7$. How many of each type of ticket were sold?

• A. $18$ children, $70$ adults
• B. $67$ children, $21$ adults
• C. $21$ children, $67$ adults
• D. $70$ children, $18$ adults

Answer 1

The correct option is B $67$ children, $21$ adults

Let $x=$ Number of children
$y=$ Number of adults

Step 1: Total number of fans are $88$.
So,
$x+y=88\dots \left(1\right)$
Step 2: Total money collected are $$553$
Money collected from chidren $=$$$4x$
Money collected from adults $=$$$7y$
So,
$4x+7y=553\dots \left(2\right)$
Multiply by $4$ into euqation $\left(1\right)$
$4x+4y=352\dots \left(3\right)$
Substracting equation $\left(3\right)$ from equation $\left(2\right)$ to eliminate $x$.

We get,
$3y=201$

$3y=\frac{201}{3}$

$\Rightarrow y=67$
Plugging $y=67$ into equation $\left(1\right)$
$x+y=88$
$x+67=88$
$x=88-67$
$\Rightarrow x=21$