CEMC Cayley, 2021

Algebra Difficulty 3.5 AMC 10/12 Find the answer Canada

Amy bought and then sold $15n$ avocados, for some positive integer $n$ . She made a profit of $100. (Her profit is the difference between the total amount that she earned by selling the avocados and the total amount that she spent in buying the avocados.) She paid $2 for every 3 avocados. She sold every 5 avocados for $4. What is the value of $n$ ?

Pick one

Solution

Amy bought and then sold $15n$ avocados.

Since she bought the avocados in groups of 3, she bought $\dfrac{15n}{3} = 5n$ groups of 3 avocados.

Since she paid $2 for every 3 avocados, she paid $\$2 \times 5n = \$10n$ .

Since she sold the avocados in groups of 5, she sold $\dfrac{15n}{5} = 3n$ groups of 5 avocados.

Since she sold every 5 avocados for $4, she received $\$4 \times 3n = \$12n$ .

In terms of $n$ , Amy’s profit is $\$12n - \$10n = \$2n$ .

Since we know that Amy’s profit was $100, we get $\$2n = \$100$ and so $2n = 100$ or $n=50$ .

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