One woman is able to buy 5 hat and 4 pairs of mittens for $30 another woman purchase 5 pairs ovens and 2 hats for 19 what are the prices

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