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There were 80 people at a play. Admission was 40$ for children and 60$ for adults. The receipts amounted to 3,800$. How many adults and children attended the play?

1 Answer

hev1 · CountryGirl

Apr 7, 2018

$30$ $30$ adults and $50$ $50$ children attended the play.

Explanation:

Let $x$ $x$ be the number of children that attended the play and let $y$ $y$ be the number of adults that attended the play.

From the information provided, we can create the following equations:
$x + y = 80$ $x+y = 80$
$40 x + 60 y = 3800$ $40x+60y = 3800$

Multiplying the first equation by $40$ $40$ :
$40 (x + y) = 80 \cdot 40$ $40(x+y) = 80*40$
$40 x + 40 y = 3200$ $40x + 40y = 3200$

Subtracting the new equation from the second equation:
$20 y = 600$ $20y = 600$
$y = \frac{600}{20}$ $y = 600/20$
$y = 30$ $y = 30$

Plugging in $30$ $30$ for $y$ $y$ in the first equation;
$x + 30 = 80$ $x+30=80$
$x = 50$ $x=50$

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