math is hard for me

Question

On a certain hot​ summer's day,

324324

people used the public swimming pool. The daily prices are

$ 1.25$1.25

for children and

$ 2.00$2.00

for adults. The receipts for admission totaled

$ 511.50 .$511.50.  

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

Answer 1

Let C = # of children attending

A = # adults

The first equation is sort of obvious:

A + C = 324 (total # of people)

Note that this means A = 324 - C, or C = 324 - A

Now we move on to money spent.

Realize that if each adult spends $2 then 2A represents the money brought in by the adults.

Similarly for children, the amount of money brought in is 1.25C.

So the following equation models the problem:

2A + 1.25C = 511.50

Since I do not particularly like working with decimals I would multiply every term by 100 to clear this equation of decimals. Essentially you are now working with pennies:

200A + 125C = 51150

At this point there are choices to make on how to solve the system of two equations and two unknowns.

I would use the fact that A = 324 - C and substitute that expression into the 2nd equation:

200(324 - C) + 125C = 51150

64800 - 200C + 125C = 51150

64800 - 75C = 51150

64800 - 51150 = 75C

75C = 13650

C = 13650/75 = 182 (this is number of children)

A = 324 - 182 = 142 (this is number of adults)

Check:

1.25(182) = $227.50

2(142) = $284

Total: $511.50