Problem:
The ratio of w to x is 4:3, the ratio of y to z is 3:2, and the ratio of z to x is 1:6. What is the ratio of w to y?
Answer Choices:
A. 4:3
B. 3:2
C. 8:3
D. 4:1
E. 16:3
Solution:
We have
yw​=xw​⋅zx​⋅yz​=34​⋅16​⋅32​=316​
from which w:y=(E)16:3​.
OR
We need to somehow link all three of the ratios together. We can start by connecting the last two ratios together by multiplying the last ratio by two.
z:x=1:6=2:12
and since
y:z=3:2
we can link them together to get
y:z:x=3:2:12
Finally, since
x:w=3:4=12:16
we can link this again to get:
y:z:x:w=3:2:12:16
so
w:y=(E)16:3​
The problems on this page are the property of the MAA's American Mathematics Competitions