Question

Marion and Justine went shopping. Marion bought 3 shirts and 4 shorts and spent $117. Justine bought 5 shorts and spent $97.50. Assume all the shorts cost the same amount. Write a system of equations representing this situation. Find the solution of the system using substitution.

Answer 1

To find the solution using substitution, we can solve the second equation for p and substitute it into the first equation. Therefore, the cost of each shirt is $13 and the cost of each shorts is $19.50.

Step-by-step explanation:

To write a system of equations representing this situation, let's use the variables s and p to represent the cost of each shirt and each shorts, respectively. We can set up the following equations:

3s + 4p = 117

5p = 97.50

To find the solution using substitution, we can solve the second equation for p and substitute it into the first equation:

p = 97.50 / 5 = 19.50

Substituting the value of p into the first equation:

3s + 4 (19.50) = 117

3s + 78 = 117

3s = 39

s = 39 / 3 = 13

Therefore, the cost of each shirt is $13 and the cost of each shorts is $19.50.