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25 Jul 2012, 00:23
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In November, a company sold 3,000 units of Model A and 1,000 units of Model B. Model A contributed 60% to the company's total monthly sales revenue in dollars, while Model B contributed the remaining 40%. If the company had sold 1,000 fewer units of Model A than they actually did, what percentage of the total monthly sales revenue in dollars would have been attributed to Model A?
A. 48
B. 50
C. 52
D. 54
E. 55
M15-34
A. 48
B. 50
C. 52
D. 54
E. 55
M15-34
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Let \(S\) denote the total November sales of the company. The price of an item of model A = \(0.6*\frac{S}{3000}\) ; the price of an item of model B = \(0.4*\frac{S}{1000}\) . If the company had sold 2000 items of model A, the revenue from sales of model A would have amounted to \(0.6*\frac{S}{3000}*2000 = 0.6S*\frac{2}{3} = 0.4S\) which is equal to the revenue from sales of model B. So, in the hypothetical case described in the stem, the two models would have accounted for 50% of the monthly sales each.
In the above explanation, when the final calculation gives you 0.4S how is that 50% of S shouldn't that be 40%??
In the above explanation, when the final calculation gives you 0.4S how is that 50% of S shouldn't that be 40%??
25 Jul 2012, 02:56
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teal
It is better to express total sale in terms of sales from both models.
Denote by A the price of one item of model A, and by B the price of an item of model B. Then we can write:
3000A / (3000A+1000B) = 0.6, from which we get that 2A = B.
So, if finally only 2000 items of model A were sold, then we get 2000A / (2000A + 1000B) = B / (2B) = 0.5.
When you change the number of items of model A, you automatically change the total sales, so you should not compare sales from model A to the initial total sale.
Initially, total sale was 3000A + 1000B, then the total sale is assumed to be 2000A + 1000B.
General Discussion
22 Feb 2024, 05:11
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Official Solution:
In November, a company sold 3,000 units of Model A and 1,000 units of Model B. Model A contributed 60% to the company's total monthly sales revenue in dollars, while Model B contributed the remaining 40%. If the company had sold 1,000 fewer units of Model A than they actually did, what percentage of the total monthly sales revenue in dollars would have been attributed to Model A?
A. 48
B. 50
C. 52
D. 54
E. 55
Suppose the total sales revenue in November was $100. In this case, Model A contributed $60 and Model B contributed $40.
If the company had sold 1,000 fewer units of Model A than they actually did, it would have sold only 2,000 units of Model A. This is 2/3 of the units of Model A that were actually sold. Consequently, Model A would have contributed 2/3 of its original contribution, amounting to $40. In this scenario, the total revenue would have been $40 + $40 = $80. Therefore, 50% of the total monthly sales revenue in dollars would have been attributed to Model A.
Answer: B
In November, a company sold 3,000 units of Model A and 1,000 units of Model B. Model A contributed 60% to the company's total monthly sales revenue in dollars, while Model B contributed the remaining 40%. If the company had sold 1,000 fewer units of Model A than they actually did, what percentage of the total monthly sales revenue in dollars would have been attributed to Model A?
A. 48
B. 50
C. 52
D. 54
E. 55
Suppose the total sales revenue in November was $100. In this case, Model A contributed $60 and Model B contributed $40.
If the company had sold 1,000 fewer units of Model A than they actually did, it would have sold only 2,000 units of Model A. This is 2/3 of the units of Model A that were actually sold. Consequently, Model A would have contributed 2/3 of its original contribution, amounting to $40. In this scenario, the total revenue would have been $40 + $40 = $80. Therefore, 50% of the total monthly sales revenue in dollars would have been attributed to Model A.
Answer: B
