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Swimming Pool On a certain hot summer's day, 322 people used the public swimming pool. The daily prices are
$1.50 for children and
$2.00 for adults. The receipts for admission totaled
$544.00. How many children and how many adults swam at the public pool that day?
There were
◻ children at the public pool.

Swimming Pool On a certain hot summer's day, $322$ people used the public swimming pool. The daily prices are $\$1.50$ for children and $\$2.00$ for adults. The receipts for admission totaled $\$544.00$ . How many children and how many adults swam at the public pool that day? There were $\square$ children at the public pool.

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Multi-step word problems

Full solution

Q. Swimming Pool On a certain hot summer's day,

322

people used the public swimming pool. The daily prices are

\$1.50

for children and

\$2.00

for adults. The receipts for admission totaled

\$544.00

. How many children and how many adults swam at the public pool that day? There were

\square

children at the public pool.

Define variables: Step $1$ : Define variables for the number of children and adults. $\newline$ Let $c$ = number of children, $a$ = number of adults. $\newline$ Total people = $c + a = 322$
Set up equation: Step $2$ : Set up the equation for total receipts. $1.50c + 2.00a = 544.00$
Solve system of equations: Step $3$ : Solve the system of equations. $\newline$ From Step $1$ : $a = 322 - c$ $\newline$ Substitute into the receipt equation: $\newline$ $1.50c + 2.00(322 - c) = 544$ $\newline$ $1.50c + 644 - 2.00c = 544$ $\newline$ $-0.50c = -100$
Solve for c: Step $4$ : Solve for c. $\newline$ $c = \frac{-100}{-0.50}$ $\newline$ $c = 200$
Find number of adults: Step $5$ : Find the number of adults using the value of $c$ . $\newline$ $a = 322 - 200$ $\newline$ $a = 122$

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