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Sagot :
Emily: 12 blueberry
13 pumpkin
total: $278
Adam: 11 blueberry
1 pumpkin
total: $102
This is a system of 2 equations with 2 variables. Let's call:
price of blueberry pie: x
price of pumpkin pie: y
The equations are:
[tex]\begin{gathered} 12x+13y=278 \\ 11x+y=102 \end{gathered}[/tex]So we have to solve this system. I'll do it by clearing y in the second equation and replacing in into the first equation:
[tex]\begin{gathered} 11x+y=102 \\ y=102-11x \end{gathered}[/tex]And we replace into the first equation:
[tex]\begin{gathered} 12x+13y=278 \\ 12x+13(102-11x)=278 \end{gathered}[/tex]And clear this one for x:
[tex]\begin{gathered} 12x+13\cdot102-13\cdot11x=278 \\ 12x-143x=278-1326 \\ -131x=-1048 \\ x=\frac{-1048}{-131}=8 \end{gathered}[/tex]If x = 8 it means that the price of the blueberry pie is $8
Then, to find y we just have to replace this value of x into the equation we cleared for y before:
[tex]\begin{gathered} y=102-11x \\ y=102-11\cdot8 \\ y=102-88 \\ y=14 \end{gathered}[/tex]The price of the pumpkin pie is $14
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