County fair

Question

An adult pass for a county fair costs $2 more than a children's pass. When 378 adults and 214 children's passes were sold, the total revenue was $2384. Find the cost of an adult pass.

Answer 1

Here's what we know:

a = c + 2

378a + 214c = 2384

 

Since we have a value for a, we can put that into the equation:

378(c+2) + 214c = 2384

378c + 756 + 214c = 2384

592c + 756 = 2384

Subtract 756 from both sides to start isolating c:

592c = 1628

Isolate c by dividing both sides by 592:

c = 2.75

 

a = 2.75 + 2

a = 4.75

 

Now to check our answer:

378 * 4.75 + 214 * 2.75 = 2384

1795.50 + 588.50 = 2384

2384 = 2384

 

So an adult ticket is $4.75