Question For math

Question

 On a certain hot​ summer's day,

71

people used the public swimming pool. The daily prices are

$1.25

for children and

$2.50

for adults. The receipts for admission totaled

$136.25.  

How many children and how many adults swam at the public pool that​ day?

Answer 1

71 people

Total admissions sales = $136.25

Let C = the number of children

Let A = the number of adults

C + A = 71

1.25C + 2.50A = 136.25

C+ A = 71

-A -A

C = 71 - A

We will substitute (71 - A) into the second equation for C.

1.25(71 - A) + 2.50A = 136.25

88.75 - 1.25A + 2.50A = 136.25

88.75 + 1.25A = 136.25

-88.75 -88.75

1.25A = 47.50

÷ 1.25 ÷ 1.25

A = 38 adults

To find the number of children, you just plug the 38 into the first equation.

C + A = 71, so C + 38 = 71

-38 -38

C = 33 children

Check our answer:

33 + 38 = 71

71 = 71

1.25C + 2.50A = 136.25

1.25(33) + 2.50(38) = 136.25

41.25 + 95.00 = 136.25

136.25 = 136.25

Answer 2

1.25C + 2.5A = 136.25

C + A = 71

1.25C + 1.25A = 71(1.25) = 88.75, subtract from 1st equation

1.25A = 136.25 - 88.75 = 47.5

A = 47.5/1.25 = 38 adults

C = 71-38 = 33 children