Question

On a certain hot​ summer's day, 340 people used the public swimming pool. The daily prices are $1.25 for children and $2.00 for adults. The receipts for admission totaled $537.50.How many children and how many adults swam at the public pool that​ day?

Answer 1

190 children and 150 adults

Explanation:

1. 1.25x + 2y = 537.5

2. x + y = 340

Here, x represents the children and y represents the adults.

Again, the first equation represent the cost of tickets, while the second represents the number of people.

From the above equation, we can solve for x and y

From equation 2,

x + y = 340

x = 340 - y

Substitute for x in equation 1

1.25x + 2y = 537.5

Then,

1.25(340 - y) + 2y = 537.5

Expand the bracket

425 - 1.25y + 2y = 537.5

Collect like terms

-1.25y + 2y = 537.5 - 425

0.75y = 112.5

y = 150.

To get the value of x, substitute for y in equation 2

x + y = 340

x + 150 = 340

x = 340 - 150

x = 190

Therefore,

There were 190 children and 150 adults at the pool that day