When the weight of apples is increased by a factor of 4, by what factor does the total cost increase?

Both sides of the ratio is increased by a factor of four.

Step-by-step explanation:

Ratios given: Weights Costs

1 2

4 8

6 12

10 20

Each cost is the double of its weight, so the base ratio is 1:2. This is where we begin.

When you increase the weight by a factor of four, this is what that side of the ratios change to:

4:2 8:8 24:12 40:20

This changes the base ratio to 2:1. Because the base ratio isn't meant to change, what we did to one side of the ratio we must do to the other to maintain proportionality. So that means the factor of cost increase is also four.

New ratios:

4:8 8:32 24:48 40:80

we know that

The cost is directly proportional to the weight, so if the weight is increased by a factor of 4, the cost will also increase by a factor of 4.

therefore

the answer is

the total cost increase by a factor of 4