AMC 12 Mock Exam 4 Problem 4

Problem 4 of 25

A bakery sells muffins individually for $\$3$ each or in boxes of $4$ muffins for $\$10$ per box. Maya spent exactly $\$47$ on muffins at the bakery. How many muffins did she buy?

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Solution

Let Maya buy $b$ boxes and $s$ single muffins: $10b+3s=47$ with $b,s\ge0$ . Modulo $3$ , $10b\equiv b$ and $47\equiv2$ , so $b\equiv2\pmod 3$ . Since $10b\le47$ , $b\le4$ , so $b=2$ and $s=\frac{47-20}{3}=9$ . She bought $4\cdot2+9=\boxed{17}$ muffins.

Tagged: linear Diophantine word problem

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