To solve this problem, we first need to establish the equations that relate the number of apple pies (let's denote it as \( p \)) and the number of apple turnovers (denote it as \( t \)) that Matt can make with the 60 apples he has.
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It takes 5 apples to make one apple pie, so the total number of apples used for \( p \) pies is \( 5p \).
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It takes 3 apples to make one apple turnover, so the total number of apples used for \( t \) turnovers is \( 3t \).
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The total number of apples used must be less than or equal to the 60 apples Matt has, which gives us the inequality:
\[ 5p + 3t \leq 60 \]
To graph this relationship, we can rearrange the equation into slope-intercept form (\( t \) in terms of \( p \)) to understand how \( t \) and \( p \) relate:
\[ 3t \leq 60 - 5p \]
Dividing through by 3 gives:
\[ t \leq 20 - \frac{5}{3}p \]
This tells us that the graph will be a straight line with a negative slope of \( -\frac{5}{3} \), starting from the point \( (0, 20) \) on the y-axis when \( p = 0 \).
Next, we need to find the points where the line intersects the axes:
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When \( p = 0 \): \[ t = 20 \] (This is where the line intersects the y-axis.)
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When \( t = 0 \): \[ 5p \leq 60 \implies p \leq 12 \] (This is where the line intersects the x-axis.)
Summary of Points:
- The line intersects the y-axis at \( (0, 20) \).
- The line intersects the x-axis at \( (12, 0) \).
Conclusion:
From this information, you can now look at the graphs J, K, L, and M to find the one that has a straight line starting at \( (0, 20) \) and ending at \( (12, 0) \). It will also have the area below the line shaded, indicating the feasible combinations of \( p \) and \( t \) that Matt can make with his 60 apples.
If you have access to those graphs, please check which one matches the description given above.