Question

On a certain hot​ summer's day, 673 people used the public swimming pool. The daily prices are $ 1.75 for children and $ 2.25 for adults. The receipts for admission totaled $ 1366.25 .  How many children and how many adults swam at the public pool that​ day?

Answer 1

296 children and 377 adults swam at the pool that day.

Step-by-step explanation:

Given,

Number of people who used public pool = 673

Price for each child admission = $1.75

Price for each adult admission = $2.25

Total receipts for admission = $1366.25

Let,

x be the number of children tickets sold

y be the number of adult tickets sold

According to given statement;

x+y=673             Eqn 1

1.75x+2.25y=1366.25  Eqn 2

Multiplying Eqn 1 by 1.25

$1.75(x+y=673)\\1.75x+1.75y=1177.75\ \ \ Eqn\ 3$

Subtracting Eqn 3 fom Eqn 2

$(1.75x+2.25y)-(1.75x+1.75y)=1366.25-1177.75\\1.75x+2.25y-1.75x-1.75y=188.50\\0.50y=188.50$

Dividing both sides by 0.50

$\frac{0.50y}{0.50}=\frac{188.50}{0.50}\\y=377$

Putting y=377 in Eqn 1

$x+377=673\\x=673-377\\x=296$

296 children and 377 adults swam at the pool that day.

Keywords: linear equation, elimination method

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