A factory produces one type of widget

[skyjarrett12]

PROBLEM: A factory produces one type of widget. This month, the factory raised the price of each widget to X% of the original price. However, the factory only sold Y% as many widgets as last month, and the total revenue from the sale of widgets was equal for last month and this month.

In the table, identify the values of X and Y that are consistent with the information provided. Make only two selections, one in each column.

MY QUESTION: In setting up my answer to this problem, I set up the equation as V1 X P1 = V2 X P2 (i.e. V1=volume and P1=Price). The explanation sets up the equation as:

"If the revenues are equal for the two months, then:

wp = (Y/100) × (w) × (X/100) × ( p)"

I'm having a hard time understanding how they are able to arrive at that.

[ethosque]

This month,the factory "raised" the price of each widget to X% of the original price

This actually tricked me.

I thought it meant :

original price = p
new price = p + X%of p

but looking at the explanation it was simply " x/100 *p "

Please clarify this issue for me. Because of this i did not get the ans. Else i would have got it.

[tim]

ethosque, the price wasn't raised BY x%; it was raised TO x%. you need to be careful about this wording..

sky, your approach is fine, you just didn't carry it far enough. you need to recognize that V2 = y/100 * V1 and that P2 = x/100 * P1; then you'll have exactly what was given in the solution..

[ethosque]

thanks Tim. noted the wording now.. :)

[tim]

glad to help..

[skyjarrett12]

Ahhh - got ya.

Thanks Tim.

[tim]

:)

[monikanedel]

Can anyone post a fully workup to this answer, would really appreciate it!

[jnelson0612]

Can anyone post a fully workup to this answer, would really appreciate it!

Hey Monika,
We are happy to help but we like to build on the work that you've already done. Can you post what work you have done so far? Then were happy to help you get the rest of the way. :-)

[wwjdat2000]

Hello~ My first time posting and I hope I'm not violating any rule here by posting here. haha.

I did get the equation to be

V1 * P1 = V1*y/100 * P2*x/100

But when I solve the equation, I get:

100/y = x/100 => xy = 1000

What am I doing wrong??

Ty!

[RonPurewal]

I did get the equation to be

V1 * P1 = V1*y/100 * P2*x/100

^^ I'll assume the purple thing is supposed to be p1, not p2 (it's the result of replacing p2 with (x/100)p1).
It seems you understand that, since you cancelled them. Let me know if otherwise.

But when I solve the equation, I get:

100/y = x/100 => xy = 1000

What am I doing wrong??

* What are the answer choices?
* Which ones did you pick?

The problem may just be the fact that you're multiplying 100 and 100 and getting 1000. (The product of 100 and 100 is 10,000 -- you're missing a zero.)

If that's not the problem, then we'll need the answer choices to get any further with this one, because you're not going to get fixed numbers here. I.e., you're just going to get a relationship (xy = 10,000, from the looks of it), and then you're just going to have to FIND two values that satisfy that relationship (by just browsing through the choices, not by using any fancy math).

[HemantR606]

ethosque, the price wasn't raised BY x%; it was raised TO x%. you need to be careful about this wording..

sky, your approach is fine, you just didn't carry it far enough. you need to recognize that V2 = y/100 * V1 and that P2 = x/100 * P1; then you'll have exactly what was given in the solution..

I have a different problem with ethosque's question. How can we say that the price was raised to x% when the price actually fell to 50%, 62.5% or 75% of the earlier price? Shouldn't we say that the price changed to x% or the original price?

[tim]

I had a tough time finding where in the previous discussion any mention was made of the price dropping. Can you clarify please?

[HemantR606]

I had a tough time finding where in the previous discussion any mention was made of the price dropping. Can you clarify please?

Tim,

Sorry, I thought the answer options were mentioned along with the Original Problem.

3 answer options of the Original Problem gave the values of X as 60, 62.5 and 70. I think my question is clear now.

[RonPurewal]

The wording of the problem tells us that...
... x should be greater than 100
... y should be less than 100.

On these "Make only two selections, one in each column" problems, you normally have to pick both answers from among the same choices.
So, here, you'll need some choices that are greater than 100 (from which you'll pick x), and others that are less than 100 (from which you'll pick y).

Yes, it's nonsense for x to be less than 100 here. So, don't pick x less than 100.
(: