If ba=2 and cb=3, what is the ratio of a+b to b+c?

1988 AMC 12 Problem 8

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\frac ba=2

and

\frac cb=3,

what is the ratio of

a+b

b+c?

\frac13

\frac38

\frac35

\frac23

\frac34

Write both

b

and

c

as multiples of

a

Substitute those expressions into

\frac{a+b}{b+c}

We have

b=2a

and

c=3b=6a.

Therefore

\frac{a+b}{b+c}=\frac{3a}{8a}=\frac38.

Thus the correct answer is B.