Mr. Sanchez's class: 1.65p
Mr. Kelly's class: 1.36j
where p = fruit pies and j = fruit juice
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(a) Creating a system of equations
p + j = 79
1.65p + 1.36j = 118.17
are your system of equations
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(a) Solving the system of equations for p and j
Solve for p in the first equation. Subtract j from both sides.
p = 79 - j
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Plug p into the second equation.
1.65(79 - j) + 1.36j = 118.17
Distribute 1.65 inside the parentheses.
130.35 - 1.65j + 1.36j = 118.17
Combine like terms.
130.35 - 0.29j = 118.17
Subtract 130.35 from both sides.
-0.29j = -12.18
Divide both sides by -0.29.
j = 42
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Plug j into the first equation.
p + (42) = 79
Subtract 42 from both sides.
p = 37
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(b) To find out how much each class earned
Now plug in p and j into Mr. Sanchez's class and Mr. Kelly's class equations (at the top).
Mr. Sanchez's class: 1.65(37) = 61.05
Mr. Kelly's class: 1.36(42) = 57.12
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(c) To see how much more Mr. S's class earned
Subtract 57.12 from 61.05.
61.05 - 57.12 = 3.93
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(a)
p + j = 79
1.65p + 1.36j = 118.17
(b)
Mr. Sanchez's class earned more money (61.05 > 57.12).
(c)
Mr. Sanchez's class earned $3.93 more than Mr. Kelly's class.