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prealgebra intermediate

Problem

Suppose

A > B > 0

and A is

x

% greater than

B

. What is

x

?

(A)

100 (\frac{A - B}{B})

(B)

100 (\frac{A + B}{B})

(C)

100 (\frac{A + B}{A})

(D)

100 (\frac{A - B}{A})

Solution

We have that A is

x %

greater than B, so

A = \frac{100 + x}{100} (B)

. We solve for

x

. We get

\frac{A}{B} = \frac{100 + x}{100}

100 \frac{A}{B} = 100 + x

100 (\frac{A}{B} - 1) = x

100 (\frac{A - B}{B}) = x

.

100 (\frac{A - B}{B})

Final answer

A