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# Keats Library purchases a number of new books, all in the ca

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Intern
Joined: 30 Aug 2017
Posts: 1

Kudos [?]: 0 [0], given: 9

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

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30 Aug 2017, 11:48
spence11 wrote:
When dealing with ratios, proportions, and percentages don't forget that each can be satisfied by an infinite number of combinations. Take $$\frac{1}{5}$$ for example:

There could be $$1$$ biography and $$5$$ total books $$\frac{1}{5}=20\%$$

There could be $$2$$ biography and $$10$$ total books $$\frac{2}{10}=20\%$$

There could be $$3$$ biography and $$15$$ total books $$\frac{3}{15}=20\%$$

This pattern proceeds into positive infinite. MANY of the questions related to ratios, proportions, and percentages will ask you about the nature of the relationship after some change. You can use some variable multiplier to handle the fact that infinite numbers could satisfy the relationship described by the ratio, proportion, or percentage. I'll call the multiplier $$m$$ and the discrete number of biographies added $$x$$

$$\frac{m+x}{5m+x}=\frac{3}{8}$$

$$8m + 8x=15m+3x$$

$$5x=7m$$

$$\frac{x}{m}=\frac{7}{5}$$

So the multiplier is some multiple of 5 and the number of books added is the same multiple of 7.

Test that out to be sure.

$$\frac{5}{25}=20\%$$

$$\frac{5+7}{25+7}=\frac{12}{32}=\frac{3}{8}$$

So if you have $$5$$ biographies of $$25$$ total books, and you add $$7$$ biographies, you'll then have $$12$$ biographies in $$32$$ total books. This satisfies the questions constraints.

$$\frac{12}{5}-1=140\%$$

Why does 1 need to be subtracted in the last step??

Kudos [?]: 0 [0], given: 9

Intern
Joined: 06 Apr 2017
Posts: 27

Kudos [?]: 14 [0], given: 38

Re: Keats Library purchases a number of new books, all in the ca [#permalink]

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30 Aug 2017, 13:16
Because the question is asking for the percent increase not the percent of the original number.

Percent increase is given by:

$$\frac{new-old}{old}\rightarrow\frac{new}{old}-1$$

Percent difference from the original value is given by:

$$\frac{new}{old}$$

Kudos [?]: 14 [0], given: 38

Re: Keats Library purchases a number of new books, all in the ca   [#permalink] 30 Aug 2017, 13:16

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