Word Problem

Question

The admission fee at a fair is $2 for children and $4 for adults. On a certain day, 2000 people enter the fair and $6000 is collected. How many children and how many adults went to see the fair on that day?

Answer 1

c = number of children

a = number of adults

 

a + c = 2000

4a + 2c = 6000

 

Multiply top equation by 2

 

2a + 2c = 4000

4a + 2c = 6000

 

Subtract top from bottom

 

2a = 2000

a = 1000

 

One thousand adults and one thousand children attended the fair.

Answer 2

Jim, this is going to be a system of equations.

 

Let's let c = the number of children and a = the number of adults.

 

Then, we know that a + c = 2000, right?

 

Since each children's ticket is $2, then the total made on children's tickets is $2c (If they sold 2 children's tickets, then made $4 on children's tickets, because $2 x 2 = $4).

 

For the same reason, the total made on adult tickets is $4a.

 

We know that 2c + 4a = 6000.

 

Let's go back to the first equation and "solve" for either a or c.  I'll do a.

 

a = 2000 - c.  Make sense?

 

We'll now take this "value" for a and plug it into the 2nd equation for a.

 

2c + (2000 - c) = 6000

 

2c + 2000 - c = 6000

 

I bet you can solve for c from here!  Use this value of c, plug it into the first equation, and get a.

 

Hope this helps!