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If x percent of y is equal to z, then y expressed in terms of x is wha

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Bunuel
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If x percent of y is equal to z, then y expressed in terms of x is wha [#permalink] New post   30 Nov 2021, 10:00
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If x percent of y is equal to z, then y expressed in terms of x is what percent of z?

A.100x

B. 1,000x

C. 10,000x

D. \(\frac{100}{x}\)

E. \(\frac{10,000}{x}\)
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Re: If x percent of y is equal to z, then y expressed in terms of x is wha [#permalink] New post   30 Nov 2021, 10:19
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If x% of y is z, then (x/100)*y = z, and y = 100z/x. So we know that y is (100/x) times z, and we just need to write that as a percentage, which we do by multiplying by 100 (if one number is, say, 3 times another, it is 300% of the other), so the answer is 10,000/x.
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Re: If x percent of y is equal to z, then y expressed in terms of x is wha [#permalink] New post   30 Nov 2021, 13:32
100% of 100=100> X,Y,Z

Therefore, Y=100 is 100% of Z=100

Which answer using X=100 yields 100?

10000/100=100

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Re: If x percent of y is equal to z, then y expressed in terms of x is wha [#permalink] New post   07 Sep 2023, 01:09
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Bunuel wrote:
If x percent of y is equal to z, then y expressed in terms of x is what percent of z?

A.100x

B. 1,000x

C. 10,000x

D. \(\frac{100}{x}\)

E. \(\frac{10,000}{x}\)



Two different ways.

Substitution

x percent of y is equal to z => 50% of 20 is 10.
So, x=50, y=20 and z=10

We are looking for y as a % of z => \(\frac{20}{10}*100=200\)
Look for options that give you answer as 200.
\(\frac{10,000}{x}\)= \(\frac{10,000}{50}=200\)
E

Algebraic

x percent of y is equal to z => \(\frac{x}{100}*y=z\)…..(1)
We are looking for: y expressed in terms of x is what percent of z, that is y as a % of z in terms of x.
Thus, we are looking for \(\frac{y}{z}*100\) in terms of x.
From (1), \(\frac{x}{100}*y=z\) or \(\frac{y}{z}=\frac{100}{x}\)
\(\frac{y}{z}*100=\frac{100}{x}*100=\frac{10000}{x}\)

E
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Re: If x percent of y is equal to z, then y expressed in terms of x is wha [#permalink]
07 Sep 2023, 01:09
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