Question

On a certain hot​ summer's day, 232 people used the public swimming pool. The daily prices are $1.50 for children and $2.25 for adults. The receipts for admission totaled $435.75. How many children and how many adults swam at the public pool that​ day?

Answer 1

children is 115 and adult is 117

Explanation:

Given

let the number of children be x

and the number of adults be y

so

x+y=232----------------1

We are told that the daily prices are $1.50 for children and $2.25 for adults

so

1.5x+2.25y= 435.75-------------------2

Hence the system of equation for the situation is

x+y=232-----1

1.5x+2.25y= 435.75-------2

From 1 x=232-y

Put this in Eqn 2

1.5(232-y)+2.25y= 435.75

348-1.5y+2.25y= 435.75

collect like terms

-1.5y+2.25y= 435.75-348

0.75y=87.75

divide both sides by 0.75

y= 87.75/0.75

y=117

the number of adults is 117

put y= 117 in eqn 1

x+117=232

x=232-117

x=115

The number of children is 115