Bookstore fractions math problem

[chawki]

Homework Statement

A bookstore reduced the price of a book with 25%. After that the sale rose by 10%.

Homework Equations

With how many percent rose the number of sold books?

The Attempt at a Solution

i guess it's simply by 10%

 

[grey_earl]

I don't think that's calculus, so you're in the wrong forum. Any moderator: please move.
Anyway, since the sale rose by 10%, but they reduced the book price, they must have sold more than 10% more books, no? Think a bit more.

 

[chawki]

The question is clear

 

[Robert1986]

The question is clear

Yeah, the question is clear, but the work you have done isn't clear.

I would try to see how you can write an equation to model this.

 

[chawki]

well, let's assume the original price is P, and the number of sold books is x. then the revenue is P*x.

reduction by 25% means the new price is 0.75*P, and new revenue is 0.75*P*1.1x

tell me if I'm right so far!

 

[Mark44]

Homework Statement

A bookstore reduced the price of a book with 25%. After that the sale rose by 10%.

Homework Equations

With how many percent rose the number of sold books?

The Attempt at a Solution

i guess it's simply by 10%

The question is clear

I don't think the question is clear at all.

"After that the sale rose by 10%." - What does that mean? You are interpreting this to mean that after the price of the book was decreased by 25%, the number of books sold increased by 10%. If that is what they're saying, then this is really a trivial problem. They have pretty much given you the answer.

On the other hand, I believe that the problem is really saying that the revenue from these books increased by 10%. That assumption makes this a more interesting problem. Are you translating the original problem statement from some other language into English? If so, your translation might be a little off.

 

[chawki]

how they have given the answer?

was what i wrote in post #5 correct ?
maybe they meant ''same profit'' tip ?

and no i didn't translate it, i wrote it as it was given.

 

[chawki]

also, I'm thinking if our problem is similar to this one:
'' After a rise in price of petrol, the driven mileage dropped by 6.7% , however the fuel costs increased by 4.5%. By what percentage did the petrol price rise ? ''

 

[Mark44]

how they have given the answer?

What answer? None of your posts in this thread shows the answer.

was what i wrote in post #5 correct ?

I don't think so. In what you wrote, you are assuming that "the sale rose by 10%" means that 10% more books sold after the price cut. As I said before, if that is what this means, the the problem is trivial.

Furthermore, it is unclear to me what "the sale rose by 10%" actually means. A "sale" is a business transaction in which someone buys a particular item. A "sale" can also mean an event during which the prices of certain items are reduced.

maybe they meant ''same profit'' tip ?

What tip?

and no i didn't translate it, i wrote it as it was given.

Please give us all of the information for this problem, including the "same profit" tip and the answer they show.

 

[chawki]

nono i just thought it can be similar to other kind of problem but i think it's not...and that's all they gave.

 

[chawki]

I don't think the question is clear at all.

"After that the sale rose by 10%." - What does that mean? You are interpreting this to mean that after the price of the book was decreased by 25%, the number of books sold increased by 10%. If that is what they're saying, then this is really a trivial problem. They have pretty much given you the answer.

On the other hand, I believe that the problem is really saying that the revenue from these books increased by 10%. That assumption makes this a more interesting problem. Are you translating the original problem statement from some other language into English? If so, your translation might be a little off.

you said ''They have pretty much given you the answer'' i don't see it..except that 10% maybe.
what does mean : ''the the problem is trivial''

 

[chawki]

the sale rose, means simply that the number of books sold increased by 10%.

 

[Mark44]

you said ''They have pretty much given you the answer'' i don't see it..except that 10% maybe.
what does mean : ''the the problem is trivial''

If "After that the sale rose by 10%." means that the number of books sold rose by 10%, then the answer to the question "With how many percent rose the number of sold books?" is obviously 10%.

That interpretation makes the problem trivial, which means that there is no difficulty at all to the problem.

I don't believe that yours is the correct interpretation. I believe that the problem is saying (very unclearly and very poorly) that the revenues from the sales of this book increased by 10%.

In my last post I asked you to clarify some things about this problem.
1) What is the complete problem statement?
2) What hints have been provided, such as the one about the "same profit" tip you mentioned?
3) What answer does your book show?

Please answer these questions before asking any further questions.

the sale rose, means simply that the number of books sold increased by 10%.

 

[chawki]

If "After that the sale rose by 10%." means that the number of books sold rose by 10%, then the answer to the question "With how many percent rose the number of sold books?" is obviously 10%.

That interpretation makes the problem trivial, which means that there is no difficulty at all to the problem.

I don't believe that yours is the correct interpretation. I believe that the problem is saying (very unclearly and very poorly) that the revenues from the sales of this book increased by 10%.

In my last post I asked you to clarify some things about this problem.
1) What is the complete problem statement?
2) What hints have been provided, such as the one about the "same profit" tip you mentioned?
3) What answer does your book show?

Please answer these questions before asking any further questions.

you know.. i think the problem is trivial...10% works for me
i'm going to answer your questions now

1) A bookstore reduced the price of a book with 25%. After that the sale rose by 10%. With how many percent rose the number of sold books?
2) no hints were provided..i just imagined it's about same profit..because on a previous exam it was about same profit..but in that case they mentioned it...in our case they didn't.
3) if only i could have the answer the problem wasn't in a book, it was from a previous exam.

 

[Mark44]

Well, since the problem was on a previous exam, there's not so much pressure to get the right answer, but I still think that your interpretation of the problem is incorrect. I'm pretty sure that "the sale rose by 10%" refers to the revenues from the book sales, not the number of books sold.

 

[chawki]

ok, so let's assume that the sale rose by 10%" refers to the revenues, in this case..my approach on post #5 was good, wasn't?

 

[Mark44]

Here's what you had in post #5.

well, let's assume the original price is P, and the number of sold books is x. then the revenue is P*x.

reduction by 25% means the new price is 0.75*P, and new revenue is 0.75*P*1.1x

tell me if I'm right so far!

ok, so let's assume that the sale rose by 10%" refers to the revenues, in this case..my approach on post #5 was good, wasn't?

For the pre-sale revenue, yes, but not for the rest.

Our assumption now is that with the reduction in price by 25%, the revenues rose by 10%.

Let y = increase in number of books sold

Old revenue = Px
New revenue = .75P(x + y)

The new revenues are 10% more than the old revenues, so
.75P(x + y) = 1.1Px
==> .75(x + y) = 1.1x
==> .75x + .75y = 1.1x
==> .75y = (1.1 - .75)x = .35x
==> y = (.35/.75)x [itex]\approx[/itex] .47x

With the reduction in price, about 47% more books were sold.

 

[chawki]

I really don't understand why we write:
0.75*(x+y)

in my mind i see three steps,
''original status'' ----> old revenue P*x
''reduction by 25%'' ----> new revenue 0.75*P*y
''10% increase in revenue'' ----> newer revenue 1.1*(0.75*P*y)

Where I'm lost ?