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If p pencils cost c cents at the same rate, how many

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If p pencils cost c cents at the same rate, how many [#permalink] New post 16 May 2017, 07:59
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If p pencils cost c cents at the same rate, how many pencils can be bought for d dollars?

A) \(cdp\)

B) \(100 cdp\)

C) \(\frac{dp}{100c}\)

D) \(\frac{100cd}{p}\)

E) \(\frac{100 dp}{c}\)
[Reveal] Spoiler: OA

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Re: If p pencils cost c cents at the same rate, how many [#permalink] New post 18 May 2017, 13:04
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Carcass wrote:


If p pencils cost c cents at the same rate, how many pencils can be bought for d dollars?

A) \(cdp\)

B) \(100 cdp\)

C) \(\frac{dp}{100c}\)

D) \(\frac{100cd}{p}\)

E) \(\frac{100 dp}{c}\)


These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.

Let's use the INPUT-OUTPUT approach.

Pick some numbers that meet the given information.
Say p = 3 and c = 50
This means that we can buy 3 pencils for 50 cents ($0.50)

Let's also say that d = 1
This means that the question is now asking "How many pencils can be bought for 1 dollar"
If we can buy 3 pencils for 50 cents, then we can buy 6 pencils for 1 dollar

So, when p = 3, c = 50 and d = 1, the answer to our question is 6 pencils.

Now let's take each answer choice and see which one yields an OUTPUT of 6, when we input p = 3, c = 50 and d = 1

A) cdp = (50)(1)(3) = 150. We need an output of 6. ELIMINATE.

B) 100cdp = (100)(50)(1)(3) = 15000. We need an output of 6. ELIMINATE.

C) dp/100c = (1)(3)/(100)(50) = 3/5000. We need an output of 6. ELIMINATE.

D) 100cd/p = (100)(50)(1)/(3) = 5000/3. We need an output of 6. ELIMINATE.

E) 100dp/c = (100)(1)(3)/(50) = 6. BINGO!

Answer:
[Reveal] Spoiler:
E


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Re: If p pencils cost c cents at the same rate, how many [#permalink] New post 17 Sep 2018, 00:41
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Step 1 - pc - p pencils* c cents
step 2 - p pencils into d dollars --> d dollars to cents --100d
divided by no of cents --> 100pd/ c
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Re: If p pencils cost c cents at the same rate, how many [#permalink] New post 18 Mar 2019, 09:57
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Carcass wrote:


If p pencils cost c cents at the same rate, how many pencils can be bought for d dollars?

A) \(cdp\)

B) \(100 cdp\)

C) \(\frac{dp}{100c}\)

D) \(\frac{100cd}{p}\)

E) \(\frac{100 dp}{c}\)


A student asked me to solve this algebraically. So, here it goes:

p pencils cost c cents at the same rate
So, the COST PER PENCIL = c/p CENTS

ASIDE: if you're not sure how to find price per pencil, you might first examine a few examples.
For example, if 3 pencils cost 6 cents, then the cost per pencil = 2 cents (notice that 6/3 = 2)
Likewise, if 4 pencils cost 20 cents, then the cost per pencil = 5 cents (notice that 20/4 = 5)
Likewise, if 7 pencils cost 63 cents, then the cost per pencil = 9 cents (notice that 63/7 = 9)
So, if p pencils cost c cents, then the cost per pencil = c/p cents

How many pencils can be bought for d dollars?
Our price per pencils is in CENTS
So, we must convert d dollars to CENTS.
Well, d dollars = 100d CENTS

ASIDE: Once again, if you're not sure how to convert d dollars to CENTS, you might first examine a few examples.
4 dollars = 400 cents, since there are 100 cents in 1 dollar (notice that 4 x 100 = 400)
Likewise, 9 dollars = 900 cents, since there are 100 cents in 1 dollar (notice that 9 x 100 = 900)
Likewise, 15 dollars = 1500 cents, since there are 100 cents in 1 dollar (notice that 15 x 100 = 1500)
Applying the same logic, we can see that d dollars = 100d CENTS

Number of items we can buy = (amount of money we have)/(price per item)
= (100d CENTS)/(c/p CENTS)
= (100d)(p/c)
= 100dp/c

Answer: E

Cheers,
Brent
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Re: If p pencils cost c cents at the same rate, how many   [#permalink] 18 Mar 2019, 09:57
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