AMC 12 Mock Exam 4 Problem 1

Problem 1 of 25

Identical plastic cups are stacked one inside another. A stack of $12$ cups is $40$ centimeters tall, and a stack of $20$ cups is $56$ centimeters tall. How many centimeters tall is a stack of $30$ of these cups?

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Solution

Adding $8$ cups raises the stack by $56-40=16$ cm, so each additional cup adds $2$ cm. Going from $20$ to $30$ cups adds $10\cdot2=20$ cm, for a height of $56+20=\boxed{76}$ cm. (Indeed the height is $2n+16$ for $n$ cups, and $2\cdot30+16=76$ . The height is not proportional to $n$ : scaling the $12$ -cup stack proportionally gives the distractor $100$ , and scaling the $20$ -cup stack gives $84$ .)

Tagged: linear model from two data points (stacked cups)

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