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System of equations helps to solve a problem for the Thanksgiving day
Problem 1Kylie was buying pies at the store for her co-workers on Thanksgiving. She needs a total of 12 pies.
The store sells pumpkin pies for $4 a pie and apple pies for $2 a pie. If Kylie ended up spending $30 on pies alone,
how many of each pie did she purchased?
Solution
Let x represents the number of pumpkin pies that Kylie buys, and let y represents the number of apple pies.
The total number of pies purchased is x + y = 12.
The total cost is 4x + 2y = 30.
Thus you have this system of equations to solve:
x + y = 12,
4x + 2y = 30.
Solving the the first equation for y gives:
y = 12 - x
Substituting "12 - x" in place of y in the equation 4x + 2y = 30 gives:
4x + 2(12 - x) = 30,
4x + 24 - 2x = 30,
2x + 24 = 30,
2x = 6 ====> x = 3.
Thus, she has purchased 3 pumpkin pies, and 12 - 3 = 9 apple pies.
Answer. Kylie has purchased 3 pumpkin pies, and 9 apple pies.
My other lessons in this site on solving systems of two linear equations in two unknowns (Algebra-I curriculum) are
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- OVERVIEW of lessons on solving systems of two linear equations in two unknowns
Use this file/link ALGEBRA-I - YOUR ONLINE TEXTBOOK to navigate over all topics and lessons of the online textbook ALGEBRA-I.
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