Kip and Yale run separate mining companies in the same forest. Both pollute the river flowing through the forest with debris from their work. In the table below, the first row shows the current level of debris that makes its way into the river from their work. The following table set out information that shows how much it would cost each company to reduce its pollution by additional increments of 10 pounds.

Kip

Yale

Current debris in pounds

60

80

Cost of reducing debris by 10 pounds

$5

$2

Cost of reducing debris by a second 10 pounds

$10

$4

Cost of reducing debris by a third 10 pounds

$15

$6

Cost of reducing debris by a fourth 10 pounds

$20

$8

Cost of reducing debris by a fifth 10 pounds

$25

$10

If each mining company is forced to cut its debris in half, the respective cost to Kip and Yale will be

Question

Kip and Yale run separate mining companies in the same forest. Both pollute the river flowing through the forest with debris from their work. In the table below, the first row shows the current level of debris that makes its way into the river from their work. The following table set out information that shows how much it would cost each company to reduce its pollution by additional increments of 10 pounds.

Kip

Yale

Current debris in pounds

60

80

Cost of reducing debris by 10 pounds

$5

$2

Cost of reducing debris by a second 10 pounds

$10

$4

Cost of reducing debris by a third 10 pounds

$15

$6

Cost of reducing debris by a fourth 10 pounds

$20

$8

Cost of reducing debris by a fifth 10 pounds

$25

$10

If each mining company is forced to cut its debris in half, the respective cost to Kip and Yale will be

BlackTom AI · Accepted Answer

The problem asks for the total cost for each company to cut its debris in half.
First, establish the halved debris amounts: Kip's current debris is 60 pounds, so half is 30 pounds. Yale's current debris is 80 pounds, so half is 40 pounds.
Now compute the costs for Kip to reduce by 30 pounds in increments of 10 pounds. The listed costs for Kip are: for the first 10 pounds, $5; the second 10 pounds, $10; the third 10 pounds, $15. Adding these together gives 5 + 10 + 15 = $30. Since Kip must reduce by three increments of 10 pounds, the total is $30.
Next, calculate Yale’s costs to reduce by 40 pounds (four increments of 10 pounds). Yale’s incremental costs are $2, $4, $6, and $8 for the first through fourth increments respectively. Summing these: 2 + 4 + 6 + 8 = $20. Therefore Yale’s total is $20 for the 40-pound reduction.
Now evaluate the other options to see where they diverge:
Option 1 claims Kip $30 and Yale $12. While Kip’s $30 matches the correct kip total, Yale’s $12 would correspond to only 6 pounds of reduction (or mis-summing the increments), which is inconsistent with a 40-pound reduction and the given step costs.
Option 2 lists Kip $5 and Yale $2 as the total costs. These figures match only the first incremental cost for each company, not the full required reductions, so they underestimate the total required costs for halving.
Option 3 states Kip $10 and Yale $4. This again reflects only the initial increment costs and ignores the subsequent 10-pound reductions, underestimating the total for the full halving.
Option 4 provides Kip $30 and Yale $20, which align with summing Kip’s three increments (5 + 10 + 15 = 30) and Yale’s four increments (2 + 4 + 6 + 8 = 20). This matches the required reductions to half for both companies.
In summary, only the combination Kip $30 and Yale $20 properly accounts for the full 30-pound reduction for Kip and the full 40-pound reduction for Yale using the provided incremental costs.

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