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 rateSo, the COST PER PENCIL =

c/p CENTSASIDE: 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 centsHow 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 CENTSASIDE: 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 CENTSNumber 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

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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