Question

You are at a festival and notice a lady is making winter wear by knitting. She sells five hats and three scarves for a total cost of $99 while three hats and five scarves cost $85. What is the cost of one hat and one scarf

Answer 1

Cost of Hats = $15

Cost of Scarves = $8

Explanation:

Let

Cost of Hats = x

Cost of Scarves = y

5x + 3y = 99 (1)

3x + 5y = 85 (2)

Multiply (1) by 5 and (2) by 3

25x + 15y = 495

9x + 15y = 255

Subtract

25x - 9x = 495 - 255

16x = 240

Divide both sides by 16

x = 240 / 16

= 15

x = $15

Substitute x = 15 into

5x + 3y = 99

5(15) + 3y = 99

75 + 3y = 99

3y = 99 - 75

3y = 24

y = 24/3

= 8

y = 8

Cost of Hats = $15

Cost of Scarves = $8