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Difficulty:
95%
(hard)
Question Stats:
33% (02:59) correct
67%
(02:37)
wrong
based on 58
sessions
History
Date
Time
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Not Attempted Yet
Malcolm’s is a store that sells only furniture and food. Over the last five years, its furniture sales have decreased by 50%, whereas its food sales have increased by 50%. Its total sales over the same period have decreased by 20%. Over the next five years, furniture sales will again decrease by 50% and food sales will again increase by 50%. What will be the percent change in sales over the next five years?
A. −20%
B. −15%
C. −6.25%
D. 0%
E. +6.25%
A. −20%
B. −15%
C. −6.25%
D. 0%
E. +6.25%
25 Mar 2026, 04:25
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Deconstructing the Question
Furniture decreases by 50% → multiply by 0.5
Food increases by 50% → multiply by 1.5
Total decreases by 20% → multiply by 0.8
Let total initial sales be \(100\).
Let furniture be \(x\), food be \(100 - x\).
Step-by-step
After 5 years:
\(0.5x + 1.5(100 - x) = 80\)
\(0.5x + 150 - 1.5x = 80\)
\(150 - x = 80\)
\(x = 70\)
So initial:
\(furniture = 70\), \(food = 30\)
After another 5 years:
Furniture:
\(70 \to 35 \to 17.5\)
Food:
\(30 \to 45 \to 67.5\)
Total:
\(17.5 + 67.5 = 85\)
Compare to original \(100\):
\(85 = -15\%\)
Answer B
Furniture decreases by 50% → multiply by 0.5
Food increases by 50% → multiply by 1.5
Total decreases by 20% → multiply by 0.8
Let total initial sales be \(100\).
Let furniture be \(x\), food be \(100 - x\).
Step-by-step
After 5 years:
\(0.5x + 1.5(100 - x) = 80\)
\(0.5x + 150 - 1.5x = 80\)
\(150 - x = 80\)
\(x = 70\)
So initial:
\(furniture = 70\), \(food = 30\)
After another 5 years:
Furniture:
\(70 \to 35 \to 17.5\)
Food:
\(30 \to 45 \to 67.5\)
Total:
\(17.5 + 67.5 = 85\)
Compare to original \(100\):
\(85 = -15\%\)
Answer B
31 Mar 2026, 19:31
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Hi kevincan can you please change the question stem, because as per the official answer posted, the question of percent change is not aligning either make it more clear that you are asking for total change from the whole 10 yr or change the OA to D which is close to 6.25%. Thanks in advance
kevincan
