teal wrote:

In the month of November, a company sold 3000 items of model A and 1000 items of model B. Items of model A accounted for 60% of the company's monthly sales while items of model B accounted for 40% of the monthly sales. If the company had sold 1000 items of model A less than it actually did, what percent of the total monthly sales would have been attributed to model A?

48

50

52

54

55

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%??

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.

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PhD in Applied Mathematics

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