Question

Tickets to the zoo cost $4 for children, $5 for teenagers and $6 for adults. In the high season, 1200 people come to the zoo every day. On a certain day, the total revenue at the zoo was $5300. For every 3 teenagers, 8 children went to the zoo. How many teenagers went to the zoo?
a. 100 teenagers
b. 200 teenagers
c. 300 teenagers
d. 400 teenagers

Answer 1

I know these three things:

6a + 5t + 4c = 5300
a + t + c = 1200
(8/3)t = c

but I have no idea how to solve for the answer.

Answer 2

Okay, well this is a little hard.

Answer 3

you can start by substituting (8/3)t for c in the first two equations

Answer 4

then you will have a system of two equations in two unknowns

Answer 5

a + t + ((8/3)t) = 1200
Would be the new combined equation right?

Answer 6

For "mechanical" solve of system linear equations try wolfram|Alpha or some web calculator i.e:

http://www.hackmath.net/en/calculator/solving-system-of-linear-equations?input=6a+%2B+5t+%2B+4c+%3D+5300%0D%0Aa+%2B+t+%2B+c+%3D+1200%0D%0A%288%2F3%29t+%3D+c&submit=Calculate

so right answer is c (t=300)

Process of solving is simple - eliminate one variable by one and you get simple equation with one unknown. And than back substitute and calculate other unknowns.

Answer 7

Wolfram is a personal favorite of mine as far as educational help site go.

I understand that I need to do the process of solving, but the problem I keep running into is that I'm not exactly sure how to begin eliminating the variables. I know that 'c' is essentially (8/3)t which can substituted in for c in the equation to make
a + t + ((8/3)t) = 1200
but I'm not sure where to go from there.

Answer 8

eliminate c:
a + t + ((8/3)t) = 1200
6a + 5t + 4(8/3)t = 5300

So:
a + 11/3 t = 1200
6a + 47/3 t = 5300

express a = 1200 - 11/3 *t

6(1200 - 11/3 *t ) + 47/3t = 5300
1900 -22 t + 47/3t = 0
1900 = 19/3 * t
t = 300

back to "a" a = 1200 - 11/3 *t = 1200 - 11/3*300 = 100
and back to "c" : c = 8/3 t = 800