Answer:
The cost of 1 hat = $2.24
The coat of 1 pair of oven mitten = $2.06
Step-by-step explanation:
Let us assume the cost of 1 hat = $ x
The cost of 1 pair of oven mitten = $y
Case 1: 5 hat and 4 pairs of mittens for $30
Cost of 5 hats =5 x ( cost of 1 hat) = 5 x = $ (5 x)
Cost of 4 mittens =4 x ( cost of 1 mittens) = 4 (y) = $ (4 y)
Total cost of 5 hats + 4 mittens = 5x + 4 y
⇒ 5 x + 4 y = $30 ....... (1)
Case 2: 2 hat and 5 pairs of mittens for $30
Cost of 2 hats =2 x ( cost of 1 hat) = 2 x = $ (2 x)
Cost of 5 mittens =5 x ( cost of 1 mittens) = 5 (y) = $ (5 y)
Total cost of 2 hats + 5 mittens = 2 x + 5 y
⇒2 x + 5 y = $19 ....... (2)
Now, solving (1) and (2) , we get:
5 x + 4 y = $30 (multiply by -2)
2 x + 5 y = $19 (multiply by 5)
Add both equations, we get:
-10 x - 8 y + 10 x + 25 y = -60 + 95
or, 17 y = 35
or, y = 35/17 = 2.05
or, y = $2.06
Now, 5 x + 4y = 30
⇒ 5 x + 4 (2.06) = 30
or, 5 x = 30 - 8.24 = 21.76
so, x = 21.76/5 = 2.24
or, x = $2.24
Hence, the cost of 1 hat = $2.24
And the coat of 1 pair of oven mitten = $2.06
