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26 May, 12:05

A bakery ordered 20 bags of flour and 16 pounds of butter on a Monday cost of $110. On Tuesday they bought 30 bags of flour and 12 pounds of butter for a cost of 120. Write a system of equations that could be used to find the cost of one bag of flour and one pound of butter?

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  1. 26 May, 14:24
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    20x + 16y = 110

    30x + 12y = 120

    Substitution method. I'll take the 2nd equation and solve for y.

    12y = 120-30x

    y = 10 - 2.5x

    Plug in this value for y into the first equation and solve for x.

    Plugin: 20x + 16 (10-2.5x) = 110

    Simplify: 20x + 160 - 40x = 110

    Simplify more: 160-20x = 110

    Subtract 160 from both: - 20x = 110-160

    Simplify: - 20x = - 50

    Divide: x = - 50/-20

    x = 2.5

    Take this value and plug back into the first equation.

    y = 10 - 2.5x

    Plugin: y = 10-2.5 (2.5)

    Simplify: y = 10-6.25

    Solve: y = 3.75

    x=2.5, y=3.75

    Verify the correctness by plugging both values into both formulas.

    20x + 16y = 110

    20 (2.5) + 16 (3.75) = 110

    50 + 60 = 110? True

    30x + 12y = 120

    30 (2.5) + 12 (3.75) = 120

    75 + 45 = 120? True

    So the price of flour per pound: 2.5

    Price of butter per pound: 3.75
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