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Difficulty: HardPercents and Percent Change

The table below shows the initial number of tomato plants and pepper plants in two agricultural fields, Field A and Field B, at the start of a crop monitoring study.

FieldTomato plantsPepper plants
Field A150150100100
Field B200200300300

During the study:
- The total number of plants in Field A increased by 20%20\%, and the number of tomato plants in Field A increased by 30%30\%.
- The total number of plants in Field B increased by 10%10\%, and the number of pepper plants in Field B increased by 15%15\%.

What was the percent increase in the total number of pepper plants across both fields combined from the start to the end of the study?

  1. A
    10.0%
  2. B
    11.1%
  3. 12.5%Answer
  4. D
    16.7%

Answer

12.5%
The correct option is 12.5%. The initial combined number of pepper plants is 100+300=400100 + 300 = 400. In Field A, the total number of plants increases by 20% from 250 to 300, while the tomato plants increase by 30% from 150 to 195. This leaves 300−195=105300 - 195 = 105 pepper plants in Field A at the end of the study. In Field B, the number of pepper plants increases by 15% from 300 to 345. Combining the final counts gives 105+345=450105 + 345 = 450 pepper plants. The total increase of 50 pepper plants relative to the initial combined count of 400 represents a 50400×100%=12.5%\frac{50}{400} \times 100\% = 12.5\% increase.

Step-by-Step Solution

1
Calculate the initial total number of plants in Field A and the initial combined number of pepper plants.
Field A initial total is 150+100=250150 + 100 = 250 plants. The initial combined number of pepper plants across both fields is 100+300=400100 + 300 = 400 plants.
Establishing the initial baseline values is necessary to compute final changes.
2
Determine the final number of pepper plants in Field A.
The final total in Field A is 250×1.20=300250 \times 1.20 = 300 plants. The final number of tomato plants in Field A is 150×1.30=195150 \times 1.30 = 195 plants. Therefore, the final number of pepper plants in Field A is 300−195=105300 - 195 = 105 plants.
This isolates the final number of pepper plants contributed by Field A since the percent increase was given for the total and for tomato plants.
3
Determine the final number of pepper plants in Field B.
The final number of pepper plants in Field B is 300×1.15=345300 \times 1.15 = 345 plants.
Applying the direct percentage increase of 15% to the initial Field B pepper plants gives their final count.
4
Calculate the combined final number of pepper plants and the percent increase.
The final combined number of pepper plants is 105+345=450105 + 345 = 450 plants. The net increase is 450−400=50450 - 400 = 50 plants. The percent increase is 50400×100%=12.5%\frac{50}{400} \times 100\% = 12.5\%.
Dividing the change in the target quantity by its original combined base yields the combined percent change.

Key Concept

Weighted percent change and finding missing values using totals and subcategory percentages
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Topics

Percents and Percent Change

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