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prealgebra intermediate

Problem

The ratio of

w

to

x

is

4 : 3

, of

y

to

z

is

3 : 2

and of

z

to

x

is

1 : 6

. What is the ratio of

w

to

y

?

(A)

1 : 3

(B)

16 : 3

(C)

20 : 3

(D)

27 : 4

Solution

Converting from ratios to fractions

\frac{w}{x} = \frac{4}{3}

,

\frac{y}{z} = \frac{3}{2}

,

\frac{z}{x} = \frac{1}{6}

\frac{y}{z} \cdot \frac{z}{x} = \frac{3}{2} \cdot \frac{1}{6}

\frac{y}{x} = \frac{1}{4}

\frac{( \frac{w}{x} )}{( \frac{y}{x} )} = \frac{\frac{4}{3}}{\frac{1}{4}}

\frac{w}{y} = \frac{16}{3}

w

to

y

is

16 : 3

16 : 3

Final answer

B