Problem Solving

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?

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OA - B

Not sure if I'm understanding this.

A company sold 3000 A items, and 1000 B items for a total of 4000 A + B items. If A makes up 60% of the total then 60% of 4000 = 3000, which it obviously doesn't... There's a 600 item discrepancy

I can't think there are any other sales being made if both of those account for 100% of the monthly sales...

Am I missing something?

We are looking for revenue, so let x = price of unit A, y = price of unit y.

We know that Item A's revenues account for 60% of total revenues.

Revenue A = 3000x, Revenue B = 1000y

60% = Revenue A / (Revenue A + Revenue B) = 3000x / (3000x + 1000y) which simplifies to 3x/(3x + y) = 0.60

solve for x: x = (1/2)*y = 0.5y (which remember, is Price of x)

so now its asking you what the percentage of sales of A would be when you have 2000 units of A:

percentage of total revenue = Rev A / (Rev A + Rev B) = 2000x / (2000x + 1000y) = 2000(0.5y) / (2000(0.5y) + 1000y) = 1000y/(1000y + 1000y) = 1/2 = 50%

Choice B.

Model A costs x dollars each.

Model B costs y dollars each.

3/5(3000x+1000y)=3000x--->1800x+600y=3000x-->y=2x

2/5(3000x+1000y)=1000y

1000 items less of model A than the company sold before= 2000 models.

2000x+1000y equals the total number of models sold. We know that y=2x, so let's substitute that into the expression above.

2000x+1000(2x)=2000x+2000x

2000x/4000x=1/2

1.Revised sales of A - 2000
2.total sales remains ( as no change has been indicated) - 4000
3. What % does A make up - 2000/4000*100 = 50%

Answer choice B