A percent decrease tells you how much of the original amount may remain. For an energy limit, compare the entire month's usage with that reduced amount: add what has already been used to what may still be used. A reduction of “at least” the stated percent allows an exact match, so the consumption limit uses an inclusive inequality. You don't need to calculate the limit to choose it.
Hints
- Hint 1
The monthly average is the base, the amount the percent is taken of. A reduction of at least 15% means the plant may use no more than the percent left after that reduction. What percent is left?
- Hint 2
April's usage includes both time periods: the energy already used and the energy used during the rest of the month. Since represents the latter, what expression gives the whole month's usage?
- Hint 3
An inclusive limit allows the value right at the boundary. A reduction of exactly still meets a goal of at least . Which inequality symbol includes that boundary without allowing more energy use?
Step-by-step
Compare the monthly total with the limit
Step 1Find the fraction of energy allowed
No Desmos needed. You're choosing an inequality, not calculating its numerical limit. The average monthly usage is the whole . To reduce it by at least , the plant can use at most the part left:
As a multiplier, . This percent applies to the original monthly average of kWh.
- Step 2
Count the whole month's usage
The plant has used kWh, and is what it can use afterward. So the monthly total is:
Add, rather than subtract: using more energy during the rest of April raises the month's total.
- Step 3
Set the inclusive upper limit
An exact reduction meets the goal, so the boundary counts. April's total must be no greater than times the monthly average:
Compare the whole month's usage with the reduced whole-month limit. The maximum allowable reaches equality, which includes. Choice A.