
Meghan D. answered 01/29/20
Patient and Creative Math Tutor Specializing in Test Prep Skills
So the first thing you want to do in these types of questions is identify the variables - what don't you know?
The problem gives how many adult tickets, child tickets and the total earned per day but they didn't give ticket prices. So those are our variables, let's say adult = x; child = y.
Then you want to identify your equations. Using what they gave you, the two equations become:
14x + 14y = 280
7x + 8y = 154
Solving an equation with only one variable would be a lot easier so let's solve the first equation for x.
First, get the x by itself on one side of the equation
14x +14y = 280
-14y -14y
------------------------
14x = 280 - 14y
Now get rid of that 14, the opposite of multiplication is division
14x = 280 - 14y
/14 /14 /14
------------------------------
x = 20 - y
This equation still has two variables, which we can't solve. What we can do is substitute the value of x we just found (20-y) into the second equation. That will give us an equation with only one variable (y)
7x + 8y = 154
7(20-y) + 8y = 154
Multiply the 7 by everything inside the parenthesis: 7 *20 = 140 and 7* -y = -7y
140-7y + 8y = 154
Consolidate those y's: -7y +8y = y
Then get that y by itself
140 + y = 154
-140 -140
------------------------
y = 14
We found the value for y! Now that it's a known variable let's go back to that first equation, which we reduced to x = 20 - y
Sub in the value we just found for y
x = 20 - 14
x = 6
So last thing you should always do is check the math! Plug in the x and y values to the two equations we got from the problem. Make sure it adds up
14(6)+ 14(14) = 280
7(6) + 8(14) = 154
It does! So x(adult tickets) = $6 and y(child tickets) = $14