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Zorluk: OrtaPercentages, Percent Change, and Interest

A municipal library system allocated a total annual acquisition budget of BB dollars between fiction and non-fiction titles. In the first half of the year, 60%60\% of the total budget was spent, with 70%70\% of that spent amount allocated to fiction books and the remainder to non-fiction books. In the second half of the year, the remaining budget was fully spent such that equal dollar amounts were allocated to fiction and non-fiction books. What percentage of the total annual budget BB was spent on fiction books?

  1. A
    42%42\%
  2. B
    50%50\%
  3. 62%62\%Cevap
  4. D
    72%72\%
  5. E
    82%82\%

Cevap

The total percentage of budget BB spent on fiction books is 62%62\%.
To find the total percentage of budget BB spent on fiction books, we analyze the two periods separately relative to the total budget BB. In the first half, 60%60\% of BB is spent, and 70%70\% of this spent amount goes to fiction, giving 0.70×0.60B=0.42B0.70 \times 0.60 B = 0.42 B (42%42\% of BB). In the second half, the remaining 40%40\% of BB is spent equally between fiction and non-fiction, so fiction receives 50%50\% of 40%40\%, which is 0.50×0.40B=0.20B0.50 \times 0.40 B = 0.20 B (20%20\% of BB). Adding both periods yields 42%+20%=62%42\% + 20\% = 62\% of the total annual budget BB.

Adım Adım Çözüm

1
Calculate the percentage of total budget BB spent on fiction in the first half of the year.
0.70×0.60B=0.42B0.70 \times 0.60 B = 0.42 B, which is 42%42\% of BB.
The library spent 60%60\% of budget BB, and 70%70\% of that spent portion went to fiction books.
2
Determine the remaining budget percentage for the second half of the year.
100%−60%=40%100\% - 60\% = 40\% of BB.
The remaining budget is the total budget minus the portion spent during the first half.
3
Calculate the percentage of total budget BB spent on fiction in the second half of the year.
0.50×0.40B=0.20B0.50 \times 0.40 B = 0.20 B, which is 20%20\% of BB.
The remaining 40%40\% budget was split equally between fiction and non-fiction.
4
Sum the fiction expenditures from both halves of the year.
42%+20%=62%42\% + 20\% = 62\% of BB.
Adding the contributions from both periods gives the total fraction of budget BB allocated to fiction books.

Anahtar Kavram

Multi-stage percentage change and part-of-a-part base shift calculations.
Tahmini Süre:1m 30s
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Konular

Percentages, Percent Change, and Interest

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