Examkin

Soru

Zorluk: OrtaPercentages, Percent Change, and Interest

At a clothing retailer, the wholesale cost of a leather coat was 50%50\% greater than the wholesale cost of a denim jacket. The following year, the wholesale cost of the leather coat increased by 20%20\%, while the wholesale cost of the denim jacket decreased by 10%10\%. What was the overall percentage increase in the combined wholesale cost of one leather coat and one denim jacket?

  1. A
    2%2\%
  2. B
    5%5\%
  3. 8%8\%Cevap
  4. D
    10%10\%
  5. E
    15%15\%

Cevap

An overall increase of 8%8\% in the combined wholesale cost.
Assuming an initial denim jacket cost of 100100, the leather coat costs 150150, giving an initial combined cost of 250250. After a 20%20\% increase, the coat costs 180180, and after a 10%10\% decrease, the jacket costs 9090. The new combined total is 270270. The total increase is 2020, which represents 20250=8%\frac{20}{250} = 8\% of the original combined cost.

Adım Adım Çözüm

1
Define variables for the initial costs of the items.
Let the initial cost of the denim jacket be d=100d = 100. Then the initial cost of the leather coat is 1.50d=1501.50d = 150.
Choosing a convenient base value makes calculating relative percentage changes straightforward.
2
Calculate the initial total cost and the new individual costs after price changes.
Initial total cost = 100+150=250100 + 150 = 250. New cost of leather coat = 150×(1+0.20)=180150 \times (1 + 0.20) = 180. New cost of denim jacket = 100×(1−0.10)=90100 \times (1 - 0.10) = 90.
Percentage increases and decreases must be applied to their respective starting costs.
3
Compute the new combined total cost and calculate the net percentage change.
New combined total cost = 180+90=270180 + 90 = 270. Dollar change = 270−250=20270 - 250 = 20. Net percentage increase = 20250×100%=8%\frac{20}{250} \times 100\% = 8\%.
Percent change is calculated by dividing the absolute change by the original combined base value.

Anahtar Kavram

Combined Percent Change and Weighted Base Values
Bu soruyu puanla

Konular

Percentages, Percent Change, and Interest

Bu konudan daha fazla soru