2020 AMC 10B Problems/Problem 3
The ratio of to is , the ratio of to is , and the ratio of to is . What is the ratio of to ?
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
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