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Algebra Difficulty 2.6 Junior Find the answer Canada

Each of the variables $a$ ,
$b$ , $c$ , $d$ , and $e$ represents a positive integer with the
properties that $\begin{align*} b+d &> a + d\\ c+e &> b+e\\ b+d&= c\\ a+c &= b+e\end{align*}$ Which of the variables has the
greatest value?

Pick one

Solution

Since $b + d > a + d$ , then
$b > a$ . This means that $a$ does not have the greatest value.

Since $c + e > b + e$ , then $c > b$ . This means that $b$ does not have the greatest value.

Since $b + d = c$ and each of $b$ , $c$ , $d$
is positive, then $d < c$ , which
means that $d$ does not have the
greatest value.

Consider the last equation $a + c = b +
e along with the fact that a < b
< c$.

From this, we see that $e = c +
(a-b)$.

Since $a < b$ , then $a-b$ is negative and so $e < c$ .

This means that $c$ has the greatest
value.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.