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