Answer:
The cost of one pair of sunglasses be $15 and cost of one shirt be $18.
Step-by-step explanation:
Consider the cost of one pair of sunglasses be x and cost of one shirt be y.
According to question,
Scarlet bought three pairs of sunglasses and two shirts for $81
Mathematically written as,
3x + 2y = 81 ....(1)
Also, Paula bought one pair of sunglasses and five shirts for $105
Mathematically written as,
x + 5y = 105 ....(2)
Solve (1) and (2) for x and y using elimination method,
Multiply equation (2) by 3 , we get,
3x + 15y = 315 .......(3)
Now subtract equation (1) from (3), we get,
⇒ 3x + 15y - ( 3x +2y) = 315 - 81
⇒ 3x + 15y - 3x - 2y = 315 -81
⇒ 15y - 2y = 234
⇒ 13y = 234
⇒ y = 18
Substitute y = 18 in (2) , we get,
x + 5y = 105 ⇒ x + 5(18) = 105 ⇒ x + 90 = 105 ⇒ x = 105-90 ⇒ x = 15.
Thus, the cost of one pair of sunglasses be $15 and cost of one shirt be $18.
