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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

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  1. Today, 16:54
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    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
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