To analyze the relationship between the weight of apples and their total cost, let's identify the pattern in the data provided.
From the ratio table, we have the following information:
- 1 lb of apples costs $2
- 2 lb of apples costs $4
- 4 lb of apples costs $8
- 6 lb of apples costs $12
- 10 lb of apples costs $20
Based on the provided data, we can see that the cost of apples appears to be directly proportional to their weight.
This can be confirmed with the calculations:
- Cost per pound for 1 lb: $2/1 = $2/lb
- Cost per pound for 2 lb: $4/2 = $2/lb
- Cost per pound for 4 lb: $8/4 = $2/lb
- Cost per pound for 6 lb: $12/6 = $2/lb
- Cost per pound for 10 lb: $20/10 = $2/lb
From this we can observe that the cost per pound is consistently $2.
Now, if we increase the weight of apples by a factor of 4:
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For the weight of 1 lb:
- New weight = 1 lb * 4 = 4 lb
- New cost = $2 * 4 = $8
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For the weight of 2 lb:
- New weight = 2 lb * 4 = 8 lb
- New cost = $4 * 4 = $16
-
For the weight of 4 lb:
- New weight = 4 lb * 4 = 16 lb
- New cost = $8 * 4 = $32
-
For the weight of 6 lb:
- New weight = 6 lb * 4 = 24 lb
- New cost = $12 * 4 = $48
-
For the weight of 10 lb:
- New weight = 10 lb * 4 = 40 lb
- New cost = $20 * 4 = $80
In each case, we can see that when the weight is increased by a factor of 4, the total cost also increases by the same factor of 4.
Therefore, the factor by which the total cost increases when the weight of apples is increased by a factor of 4 is 4.
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