Answer: A movie ticket is $9 while a snack is $2
Step-by-step explanation: We shall let a movie ticket be m while a snack is s. So, from the clues given, if two movie tickets and three snacks cost $24, we can write it as the following expression;
2m + 3s = 24
Also if three movie tickets and four snacks cost $35, we can as well write another expression as follows;
3m + 4s = 35.
Now we have a pair of simultaneous equations which are
2m + 3s = 24 ----------(1)
3m + 4s = 35 ----------(2)
We shall solve this by using the elimination method, since none of the variables has a coefficient of 1. We'll start by multiplying equation (1) by 3 and multiplying equation (2) by 2 (so as to eliminate the m variable)
2m + 3s = 24 -------- x3
3m + 4s = 35 ---------x2
We now arrive at the following
6m + 9s = 72--------(3)
6m + 8s = 70--------(4)
Subtract equation (4) from equation (3) and we arrive at
s = 2
Having determined that s equals 2 we can now substitute for the value of a into equation (1)
2m + 3s = 24
2m + 3(2) = 24
2m + 6 = 24
Subtract 6 from both sides of the equation
2m + 6 - 6 = 24 - 6
2m = 18
Divide both sides of the equation by 2
m= 9
Therefore one movie ticket costs $9 while one snack costs $2
