On a certain hot summer days 610 people use the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $1065. How many children and how many adults swim at the public pool that day

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absor201 absor201 · Answer 1 · 2019-11-29T13:57:27+01:00

368 children and 242 adults swam at the public pool.

Step-by-step explanation:

Let,

x be the number of children.

y be the number of adults.

Price per children = $1.25

Price per adult = $2.50

Total tickets sold = 610

Total amount = $1065

According to given statement;

x+y=610 Eqn 1

1.25x+2.50y=1065 Eqn 2

Multiplying Eqn 1 by 1.25;

[tex]1.25(x+y=610)\\1.25x+1.25y=762.5\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 3 from Eqn 2;

[tex](1.25x+2.50y)-(1.25x+1.25y)=1065-762.5\\1.25x+2.50y-1.25x-1.25y=302.5\\1.25y=302.5\\[/tex]

Dividing both sides by 1.25;

[tex]\frac{1.25y}{1.25}=\frac{302.5}{1.25}\\y=242[/tex]

Putting y=242 in Eqn 1;

[tex]x+242=610\\x=610-242\\x=368[/tex]

368 children and 242 adults swam at the public pool.

Keywords: linear equations, subtraction

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