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Algebra Difficulty 1.6 Junior Find the answer Canada

At the start of this month, Mathilde and Salah each had 100
coins. For Mathilde, this was 25% more coins than she had at the start
of last month. For Salah, this was 20% fewer coins than he had at the
start of last month. The total number of coins that they had at the
start of last month was

Pick one

Solutions — 2

Solution 1

Suppose that Mathilde had $m$
coins at the start of last month and Salah and $s$ coins at the start of last month.

From the given information, 100 is 25% more than $m$ , so $100 =
1.25m $which means that$ m =
$\dfrac{100}{1.25}$ = 80$.

From the given information, 100 is 20% less than $s$ , so $100 =
0.80s $which means that$ s =
$\dfrac{100}{0.80}$ = 125$.

Therefore, at the beginning of last month, they had a total of $m + s = 80 + 125 = 205$ coins.

Solution 2

Suppose that Mathilde had $m$
coins at the start of last month and Salah had $s$ coins at the start of last month.

From the given information, 100 is 25% more than $m$ , so $100 =
1.25m $which means that$ m =
$\dfrac{100}{1.25}$ = 80$.

From the given information, 100 is 20% less than $s$ , so $100 =
0.80s $which means that$ s =
$\dfrac{100}{0.80}$ = 125$.

Therefore, at the beginning of last month, they had a total of $m + s = 80 + 125 = 205$ coins.

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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.