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An online store sells two products: a hardcover and soft cover book of 13 Jul 2020, 04:08
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E
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An online store sells two products: a hardcover and soft cover book of sonnets. Altogether, the company earned $65,000 in profits last year on the sale of 5000 units. If their profit on the hardcover book is $5 and their profit on the soft cover version is $15, how many soft cover books did they sell?

A. 1000
B. 1500
C. 2000
D. 3500
E. 4000
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E
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An online store sells two products: a hardcover and soft cover book of 13 Jul 2020, 04:17
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Let the number of books sold be:

Hard Cover = H
Soft Cover = S

H + S = 5000 ......... (i)
5H + 15S = 65000 ........ (ii)

Solving (i) and (ii),
5*(5000 - S) + 15S = 65000
25000 - 5S + 15S = 65000
10S = 40000
S = 4000

Answer: E
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An online store sells two products: a hardcover and soft cover book of 13 Jul 2020, 05:44
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The company's average profit per unit was $13. If their profit on hardcovers is $5 and on softcovers is $15, they must have sold way more softcovers than hardcovers, because $13 is much closer to $15 than to $5. You could use alligation to quickly get an exact answer here (I won't explain that method in detail here, but the ratio of softcovers to hardcovers must be 13-5 to 15-13, or 8 to 2, from which the answer follows), but if you have a feeling for how weighted averages work, you can see almost immediately that E is the only reasonable answer.
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An online store sells two products: a hardcover and soft cover book of 13 Jul 2020, 09:14
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Sir,

IanStewart
The company's average profit per unit was $13. If their profit on hardcovers is $5 and on softcovers is $15, they must have sold way more softcovers than hardcovers, because $13 is much closer to $15 than to $5. You could use alligation to quickly get an exact answer here (I won't explain that method in detail here, but the ratio of softcovers to hardcovers must be 13-5 to 15-13, or 8 to 2, from which the answer follows), but if you have a feeling for how weighted averages work, you can see almost immediately that E is the only reasonable answer.
Show more



but the ratio of softcovers to hardcovers must be 13-5 to 15-13, or 8 to 2, from which the answer follows)

If average is 13$ per unit( 65k/5k) then most units sold are from Softcovers.

Total profit is 15$+5$ , average is 13$ and softcover units would be more than half ( which means option D or option E)

Could you please clarify why do you say softcovers to hardcovers must be 13-5 to 15-13, or 8 to 2. i am kind of lost of here.
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An online store sells two products: a hardcover and soft cover book of 13 Jul 2020, 10:32
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imSKR
Sir,

IanStewart
The company's average profit per unit was $13. If their profit on hardcovers is $5 and on softcovers is $15, they must have sold way more softcovers than hardcovers, because $13 is much closer to $15 than to $5. You could use alligation to quickly get an exact answer here (I won't explain that method in detail here, but the ratio of softcovers to hardcovers must be 13-5 to 15-13, or 8 to 2, from which the answer follows), but if you have a feeling for how weighted averages work, you can see almost immediately that E is the only reasonable answer.



but the ratio of softcovers to hardcovers must be 13-5 to 15-13, or 8 to 2, from which the answer follows)

If average is 13$ per unit( 65k/5k) then most units sold are from Softcovers.

Total profit is 15$+5$ , average is 13$ and softcover units would be more than half ( which means option D or option E)

Could you please clarify why do you say softcovers to hardcovers must be 13-5 to 15-13, or 8 to 2. i am kind of lost of here.
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Use Alligation method no confusion will prevail..........



5________15

___13___

2________ 8

1:4

Hope you get it easily now.........
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An online store sells two products: a hardcover and soft cover book of 14 Jul 2020, 04:52
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imSKR

Could you please clarify why do you say softcovers to hardcovers must be 13-5 to 15-13, or 8 to 2. i am kind of lost of here.
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I'm using the method sometimes called "alligation", which I mentioned in my post. It's a method you can use to solve weighted average problems. If you're interested in learning more about it, you could search this forum or the internet - I've posted about it a few times, and so have other people.

Briefly, alligation tells us that if we draw our averages on a number line:

---5------------------13------15-------

the ratio of the distances to the middle number will equal the ratio of the sizes of the two groups. The distances to the middle number above are 8 and 2, so the two groups are in an 8 to 2 ratio, or 4 to 1 ratio. We have more softcovers than hardcovers (because 13 is closer to 15), so the ratio of softcovers to hardcovers is 4 to 1.

But if you want to learn more about how to use that method, it would be best to see a more detailed explanation with other examples.
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