Question
Dominic went apple picking and returned home with a basket full of fresh apples. Worried that the apples might rot before he can eat them all, he plans to make pies for his friends and family to enjoy. There is a linear relationship between the number of pies Dominic makes, and the amount of apples left in the basket, in pounds. 2 4 6 8 10 12 14 16 18 20 4 8 12 16 20 24 28 32 36 40 x y Number of pies Amount of apples left in the basket (pounds) Describe the rate of change for this relationship. The amount of apples left in the basket increases decreases by 1 2 of a pound 1 pound 2 pounds 4 pounds 7 pounds 36 pounds per pie.
Answers
GPT-4o mini
To determine the rate of change in the relationship between the number of pies Dominic makes and the amount of apples left in the basket, we can analyze the data provided.
The data points are:
- 2 pies → 4 pounds
- 4 pies → 8 pounds
- 6 pies → 12 pounds
- 8 pies → 16 pounds
- 10 pies → 20 pounds
- 12 pies → 24 pounds
- 14 pies → 28 pounds
- 16 pies → 32 pounds
- 18 pies → 36 pounds
- 20 pies → 40 pounds
From this data, we can see that for every 2 additional pies made, the amount of apples left in the basket increases by 4 pounds (for example, going from 2 pies to 4 pies shows an increase from 4 pounds to 8 pounds).
To express the relationship in terms of rate of change, we can compute it as follows:
- When Dominic makes 2 pies, he has 4 pounds of apples left.
- When he makes 4 pies, he has 8 pounds left.
The change in pounds of apples is:
\[
8 \, \text{pounds} - 4 \, \text{pounds} = 4 \, \text{pounds}
\]
The change in the number of pies is:
\[
4 \, \text{pies} - 2 \, \text{pies} = 2 \, \text{pies}
\]
Now, we calculate the rate of change:
\[
\text{Rate of Change} = \frac{\text{Change in Apples}}{\text{Change in Pies}} = \frac{4 \, \text{pounds}}{2 \, \text{pies}} = 2 \, \text{pounds per pie}
\]
This means that for every pie he makes, the amount of apples left in the basket decreases by 2 pounds.
Therefore, the answer is:
**The amount of apples left in the basket decreases by 2 pounds per pie.**
The data points are:
- 2 pies → 4 pounds
- 4 pies → 8 pounds
- 6 pies → 12 pounds
- 8 pies → 16 pounds
- 10 pies → 20 pounds
- 12 pies → 24 pounds
- 14 pies → 28 pounds
- 16 pies → 32 pounds
- 18 pies → 36 pounds
- 20 pies → 40 pounds
From this data, we can see that for every 2 additional pies made, the amount of apples left in the basket increases by 4 pounds (for example, going from 2 pies to 4 pies shows an increase from 4 pounds to 8 pounds).
To express the relationship in terms of rate of change, we can compute it as follows:
- When Dominic makes 2 pies, he has 4 pounds of apples left.
- When he makes 4 pies, he has 8 pounds left.
The change in pounds of apples is:
\[
8 \, \text{pounds} - 4 \, \text{pounds} = 4 \, \text{pounds}
\]
The change in the number of pies is:
\[
4 \, \text{pies} - 2 \, \text{pies} = 2 \, \text{pies}
\]
Now, we calculate the rate of change:
\[
\text{Rate of Change} = \frac{\text{Change in Apples}}{\text{Change in Pies}} = \frac{4 \, \text{pounds}}{2 \, \text{pies}} = 2 \, \text{pounds per pie}
\]
This means that for every pie he makes, the amount of apples left in the basket decreases by 2 pounds.
Therefore, the answer is:
**The amount of apples left in the basket decreases by 2 pounds per pie.**