AMC 10 USA Math Olympiad

Ratio Problem from AMC 10B – 2020 – Problem No.3

The simplest example of power mean inequality is the arithmetic mean – geometric mean inequality. Learn in this self-learning module for math olympiad

What is Ratio ?

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.

Try this Problem from AMC 10B – 2020 – Problem No.-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


3 out of 10

Mathematics can be fun

Knowledge Graph

Ratio - Knowledge Graph

Use some hints

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……

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

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

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