Solving a Ratio Problem with Three Variables

Question

A question that just popped in my head after reading an article:

If the radius of Planet X is 16% larger than that of Earth, and Planet X has 40% the radius of Planet Y, then what is the radius of Planet Y in terms of Earth radii?

I'm having trouble trying to figure this one out. How would we solve this one?

I understand we may have to define one variable in terms of another to get the desired result, but again, I seem to be failing miserably at it.

I literally just realized that and removed it. You beat me to it! — TRX, Nov 12 '15 at 04:07

score 1 · Answer 1 · answered Oct 01 '18 at 09:11

1

We have $X = 1.16E$ and $X= 0.4Y$.

Equating these we get $1.16E = 0.4 Y \implies Y = \frac{1.16}{0.4}E = 2.9E$.

So the radius of planet $Y$ is $2.9$ Earth radii.

answered Oct 01 '18 at 09:11

MRobinson

1,692
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G. Allen · Answer 2 · 2015-11-12T04:20:05.710

0

Let $X$, $Y$ and $E$ be the radii of the two planets and Earth, respectively. Then

$X = 1.16E$

and

$X = 1.40Y$

Substitution gives you $1.16E = 1.40Y$

Solve that equation for $Y$ and you'll have the result that you're looking for.

edited Nov 12 '15 at 04:20

answered Nov 12 '15 at 04:12

G. Allen

184

x is 16% larger, not 16% of total. – fleablood Nov 12 '15 at 04:15
It was my mistake. G. Allen based this answer on the problem before I made an edit to it. Apologies. – TRX Nov 12 '15 at 04:18
Easy enough to fix. I edited my post to reflect the new wording. – G. Allen Nov 12 '15 at 04:20
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Shouldn't that be X = 0.4Y? – TRX Nov 12 '15 at 04:22

Solving a Ratio Problem with Three Variables

2 Answers2