CEMC Pascal, 2023

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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