In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six which is equivalent to 4:3.
The ratio of w to x, y to z and z to x are 4:3, 3:2 and 1:6 respectively . What is the ratio of w to y ?
A) 4:3 B) 3:2 C) 8:3 D) 4:1 E) 16 :3
American Mathematics Competition 10 (AMC 10B), 2020, Problem Number 3
Ratio
3 out of 10
Mathematics can be fun
First hint
This one is an easy sum to solve but those who are confused right now can use the first hint :
The ratio of w : x = 4 : 3 ; so we can write it \(\frac {w}{x} = \frac {4}{3}\). Similarly we can do it for the other given ratios. Try to do it......
Second Hint
I think you have already got the answer . If not then try this out .....
z : x = 1 : 6 i.e \(\frac {z}{x} = \frac {1}{6} \)
y : z = 3 : 2 i.e \(\frac {y}{z} = \frac {3}{2}\)
Final Step
This hint is the final hint as already mentioned in header :
Lets multiply each ratios :
\(\frac {w}{x} \times \frac {x}{z} \times \frac {z}{y} = \frac {4}{3} \times 6 \times \frac {2}{3} \)
After canceling out all the similar terms \(\frac {w}{y} = \frac {16}{3}\)
AMC - AIME Boot Camp... for brilliant students.
Use our exclusive one-on-one plus group class system to prepare for Math Olympiad