Question

Scarlet bought three pairs of sunglasses and two shirts for $81 and Paula bought one pair of sunglasses and five shirts for $105 What is the cost of one pair of sunglasses and one shirt?

Answer 1

the cost of one pair of sunglasses = $15

the cost of one pair of shirt = $18

Explanation:

Let 'x' be the price of a pair of sunglasses and 'y' be the price of one shirt.

To form the equation

It is given that,

Scarlet bought three pairs of sunglasses and two shirts for $81

we can write,

3x + 2y = 81 -----(1)

and Paula bought one pair of sunglasses and five shirts for $105,

We can write,

x + 5y = 105 -----(2)

To find x and y

Multiply eq(2) by 3 we get

3x + 15y = 315 ----(3)

eq(3) - eq(1) ⇒ 13y = 234

y = 234/13 = 18

eq(2) ⇒ x + 5y = 105

x + 5*18 = 105

x = 105 - 90 = 15

Therefore, the cost of one pair of sunglasses= 15 and one shirt = 18

Answer 2

The cost of one pair of sunglasses be $15 and cost of one shirt be $18.

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.