The admission fee at an amusement park is $1.50 for children and $4 for adults. 233 people entered the park, and the admission fees collected totaled 662dollars.

Question

 How many children and how many adults were admitted?

Answer 1

If you wanted to figure out the amount of money they took in, how would you do it? Wouldn't you multiply the number of people by the fee charged per person? You are given the fee charged per person so we need to determine, as asked, the number of children and the number of adults who attended.

So we can let "c" equal the number of children who attended and we can let "a" equal the number of adults who attended.

Then $1.50 multiplied by "c" added to $4.00 times "a" would give you the total or:

1.50c + 4.00a = 662

We are also told that there 233 total people who attended so adding the children and adults together gives 233 or:

c + a = 233

That means a = 233 - c

Since "a" is the same as "233 - c" (because they are equal) then we can plug in "233 - c" in place of "a" in the first equation:

1.50c + 4.00(233 - c) = 662

1.50c + 4.00•233 - 4.00c = 662 then combine like terms:

1.50c - 4.00c + 932 = 662

-2.50c = 662 - 932

-2.50c = -270 then divide both sides by -2.50 to get:

c = 108

Then, using a + c = 233, we can plug in c = 108 and get:

a + 108 = 233

a = 233 - 108

a = 125