Three stages in sequence signal successive percent changes: each percent uses the weight from the stage immediately before it. Turn each loss into a fraction retained and each gain into a fraction of the current weight, then multiply those factors in Desmos. Don't add the percentages: the discard and water absorption use different starting weights.
Hints
- Hint 1
A percent remaining is what stays after a decrease. Start with of the original weight. If roasting removes part of it, what percent remains to enter the next stage?
- Hint 2
The base of a percent is the amount it's taken of. The discard rate applies to the roasted beans, not the original beans. What fraction of the roasted weight survives?
- Hint 3
A percent increase keeps the whole current weight and adds a fraction on top. For cooling, find a multiplier greater than , then multiply all three stage multipliers.
Step-by-step
Multiply the stage-by-stage factors
Step 1Find the roasting multiplier
A multiplier is the number that turns a weight into its weight after a change. Roasting removes of the starting weight, so subtract that loss from the whole: . The roasting multiplier is .
- Step 2
Find the discard multiplier
The discarded is taken from the roasted beans, not the original beans. Subtract it from of that roasted weight: . The discard multiplier is . Each new percent uses the weight left by the stage before it.
- Step 3
Find the cooling multiplier
The water adds of the current weight, while the beans keep all the weight they already have. Add the gain to that whole weight: . The cooling multiplier is , not , which counts only the water added.
- Step 4
Write the final weight as a percent
Since compares the final weight with the original weight, take the original as weight units. Apply the three multipliers in order: . With units at the start, the final number of units is also the final percent.
- Step 5
Calculate and round
Type in Desmos. It shows , which is already to the nearest hundredth. The final usable coffee weighs of the original. Choice C.