Word problem

Question

Admission prices at a local fair were $5 for children $7 for adults. The total collected was $3379, and 587 people attended the fair. How many children and how many adults attended the fair?

Answer 1

Jenny,

There are several ways to get the answer you're looking for. Here's one approach.

 

First let's assign variables, c = # of children and a = # of adults.

 

Now let's look at what we know:

 

$5 per child to attend the fair

$7 per adult to attend the fair

$3, 379 total collected, so $5c + $7a = $3,379 and

 

We also know that (c + a) = 587... total of children and adults attended, 

 

Let's stack both equations and solve

 

5c + 7a = 3,379

c   +  a =    587

 

let's multiply the bottom expression by -5, and then add them together:

 

 5c + 7a =  3,379
-5c - 5a  = -2,935

 0c + 2a = 444

 

2a = 144, divide both sides by 2 and a (# of adults) = 122

 

Now it's easy, because

 

c + a = 587, and a = 122 so

 

c + 122 = 587, subtract 122 from both sides to get:

 

c = 587 - 122 = 465 children

 

So 122 adults and 465 children attended the fair.

 

 

I hope this helps!

 

Neal