The way to solve this question is by creating a system of equations with the information you're given.
The first set of information: "You have 50 tickets, it costs 3 to ride the ferris wheel and 5 for the roller coaster.."
# should be read as "number" or "the number of"
translates to (#tickets)= (3 times the #ferriswheelrides) + (5 times the #rollercoasterrides) = 50
Let F denote the number of ferris wheel rides and R denote the number of roller coaster rides
The first equation is: 3F + 5R = 50
Similarly, the second set of information also translates into an equation.
".. all together you ride 12 times. "
That means that the number of ferris wheel rides and roller coaster rides sum to 12
Or, in equation form, F + R =12
So the two equations that you must simultaneously solve are 3F + 5R = 50
and F + R = 12
You may solve these equations in two different ways: Through cancellation or substitution
Let's use substitution. Solve for F in the second equation. F= 12 - R
This F is the same F that is in the first equation. It is equivalent to 12 - R. In other words, it IS 12 - R.
So let us rewrite the first equation by incorporating this information via substitution. Replace F with 12-R in the first equation. 3(12-R) + 5R = 50. This equation only contains R and so now it is possible to find the value of R.
36 - 3R + 5R = 50
36+ 2R = 50
2R = 14
R = 7
And since we know that the total number of rides, F + R, is 12, we know that F must have been 5.
The question asks how many times the roller coaster was ridden. The answer is 7!
