# How well did Jean do?

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### The Problem:

Jean's mean score is 22% less than her score in biology, her biology score was 10% higher than her chemistry, her English was the same as her mathematics result, and physics was half the mathematics score and 30% points lower than the mean.

What were Jean's scores in each subject and the mean score?

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### Solution:

Let's work each statement in the question one after the other.

"Jean's mean score is 22% less than her score in biology" implies

$M=b-22$

where $M$ is her mean score and $b$ is her score in biology.

"her biology score was 10% higher than her chemistry" implies

$b=c+10$

where $c$ is her chemistry score.

"her English was the same as her mathematics result" implies

$e=m$

where $e$ is English and $m$ is maths.

"and physics was half the mathematics score and 30% points lower than the mean" gives two mathematical statements

$p=m2$

and

$p=M-30$

where $p$ is her physics score.

Now, let's consider the mean score ...

$M=m+e+b+c+p5$

Combining this with others above,

$5⁢(p+30) =2⁢p+2⁢p+M+22+b-10+p$ $5⁢p+150=5⁢p+M+12+b$ $138=M+b$ $138=b-22+b$ $b=80$ $M=b-22⇒M=48$ $b=c+10⇒c=70$ $p=M-30⇒p=18$ $p=m2⇒m=e=36$
So her scores are ...
English 36%
Mathematics 36%
Biology 80%
Chemistry 70%
Physics 18%
Mean score 48%

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