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?

Question

Chace Maxwell

Mathematics

4 April, 17:20

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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Answers (1)

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Catherine Buckley · Answer 1

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