# What percent of Juan's income is Mary's income?

For the following question

Mary's income is 60% more than Tim's income , and Tim's income is 40% less than Juan's income. What percent of Juan's income is Mary's income? (Ans=96%)

I am attempting to solve this using the following two equations, but I can't figure out what to do next. Suggestions would be appreciated

Mary = Mary + $\frac{60}{100}Tim$

Tim= Tim - $\frac{40}{100}Juan$

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Example: $A$ is 10% bigger than $B$ means that $A = (1 + 0.10)B = 1.10B$. And: $A$ is 10% less than $B$ means $A = 1 - 0.10 = 0.90B$.

Example: If I have $200$ apples and you have $300$ apples, then $300/200 = 1.50 = 1 + 0.50$, so you have $50$% more apples that I do. So that is $300 = 200 + 0.50\cdot 200$.

Let $M$ be Mary's income, $T$ be Tim's income, and $J$ be Juan's income. Then you have $M = 1.6T$ and $T = 0.6J$, so $M = 1.6\cdot 0.6J = ...$

As a sidenote: the equations that you wrote down don't really make sense. The first one, for example, would imply that Tim's income is zero (subtract Mary on both sides).

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How did you get M=1.6T isnt it suppose to be M = M + 0.6T ? – MistyD Aug 30 '12 at 13:42
@Thomas: 50% more not 150% more. And that means $300 = 200 + \frac{50}{100} \times 200$ rather than $300 \not= 300 + \frac{50}{100} \times 200$ – Henry Aug 30 '12 at 13:50
@Henry: oops. I edited – Thomas Aug 30 '12 at 13:52

"Mary = Mary + $\frac{60}{100}$Tim" is clearly wrong unless Tim = $0$. Similarly with "Tim = Tim - $\frac{40}{100}$Juan" unless Juan = $0$.

It should be "Mary = Tim + $\frac{60}{100}$Tim" and "Tim = Juan - $\frac{40}{100}$Juan" which [as Thomas says] leads to "Mary $= \left(1+\frac{60}{100}\right)\left(1-\frac{40}{100}\right)$Juan" and thus the result you want.

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Thanks that cleared a lot – MistyD Aug 30 '12 at 13:50