Brian P. answered • 03/30/17
Tutor
5.0
(203)
Chemistry, Calculus, Algebra 2, SAT/ACT, Geometry Expert UCLA Grad
There are two units to work with for this problem. One unit is the number of tickets, and the other unit is money. Having two units means needing two equations. We'll start with making the equation for the number of tickets. Let's use "A" for adult tickets, and "C" for children's tickets. Because the tickets totaled to be 600, here's the equation for the number of tickets.
A + C = 600
Next, we need to make an equation for the money part of it. Each adult ticket costs $1.50, and each children's ticket costs $1.00. Use these values as the coefficients for the respective variables. The total amount of money was $800.
1.50A + 1.00C = 800
To make this equation look nicer, I'll do a bit of simplification of the decimal values. 1.50A is the same as 1.5A, and 1.00C is the same as a plain old "C."
1.5A + C = 800
Now let's look at the two equations side-by-side to see what we're dealing with here.
A + C = 600
1.5A + C = 800
Each equation has two variables, meaning we can't really solve it. Luckily, there's a technique called "substitution." This technique will get one of the equations all in terms of one variable to making solving much nicer. Pick any equation, and get one of the variables alone. In this case, I'll pick the second equation and get "C" alone.
1.5A + C = 800
C = 800 - 1.5A
Because C = 800 - 1.5A, substitute this expression where the "C" is in the first equation.
A + C = 600
A + (800 - 1.5A) = 600
-0.5A + 800 = 600
-0.5A = -200
A = 400
Awesome, now that we solved for one of the variables and got A = 400, that will make solving for "C" much better. Pick any of the equations, substitute in A = 400, and solve for "C." I'll choose the first equation.
A + C = 600
400 + C = 600
C = 200
A = 400 and C = 200, so there were a total of 400 adult tickets and 200 children tickets.
I hope this helps, and good luck with your math class!
