Examkin

Question

Difficulty: HardFractions, Decimals, and Percentages

A coffee artisan roasts a 120120-pound batch of green coffee beans. During the roasting process, the beans lose 15%15\% of their total weight due to moisture evaporation. Next, 18\frac{1}{8} of the roasted weight is removed during quality control sorting. Finally, the remaining high-quality roasted beans are packaged into small bags that each hold 0.750.75 pounds of coffee. How many full bags of roasted coffee can be produced from this batch?

  1. A
    116116
  2. 119119Answer
  3. C
    122122
  4. D
    136136
  5. E
    161161

Answer

The total number of full bags of roasted coffee that can be produced is 119119.
To find the number of bags, calculate the remaining weight step-by-step. First, 15%15\% of 120120 pounds is 1818 pounds, leaving 102102 pounds of roasted coffee. Next, 18\frac{1}{8} of 102102 pounds is 12.7512.75 pounds, leaving 89.2589.25 pounds of high-quality coffee. Dividing 89.2589.25 by 0.750.75 pounds per bag yields exactly 119119 full bags.

Step-by-Step Solution

1
Calculate the weight lost during roasting
15%15\% of 120 lbs=0.15×120=18 lbs120\text{ lbs} = 0.15 \times 120 = 18\text{ lbs}
The beans lose 15%15\% of their initial weight due to evaporation.
2
Determine the remaining weight of roasted beans
120 lbs−18 lbs=102 lbs120\text{ lbs} - 18\text{ lbs} = 102\text{ lbs}
Subtract the weight lost during roasting from the starting weight.
3
Calculate the weight removed during quality control
18×102 lbs=12.75 lbs\frac{1}{8} \times 102\text{ lbs} = 12.75\text{ lbs}
Quality control removes 18\frac{1}{8} of the roasted weight.
4
Determine the final usable weight of coffee beans
102 lbs−12.75 lbs=89.25 lbs102\text{ lbs} - 12.75\text{ lbs} = 89.25\text{ lbs}
Subtract the rejected beans from the roasted weight.
5
Calculate the number of 0.750.75-pound bags produced
89.25÷0.75=119 bags89.25 \div 0.75 = 119\text{ bags}
Divide the total usable weight by the capacity of a single bag.

Key Concept

Sequential application of percentages and fractions to remaining quantities
Estimated Time:2m 0s
Rate this question

Topics

Fractions, Decimals, and Percentages

More questions from this topic