2020 AMC 10B Problems/Problem 3
Problem 3
The ratio of to
is
, the ratio of
to
is
, and the ratio of
to
is
. What is the ratio of
to
?
Solution 1
WLOG, let and
.
Since the ratio of to
is
, we can substitute in the value of
to get
.
The ratio of to
is
, so
.
The ratio of to
is then
so our answer is
~quacker88
Solution 2
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.
, and since
, we can link them together to get
.
Finally, since , we can link this again to get:
, so
~quacker88