2012 AMC 8 Problems/Problem 1

Problem

Rachelle uses 3 pounds of meat to make 8 hamburgers for her family. How many pounds of meat does she need to make 24 hamburgers for a neighborhood picnic?

$\textbf{(A)}\hspace{.05in}6 \qquad \textbf{(B)}\hspace{.05in}6\dfrac23 \qquad \textbf{(C)}\hspace{.05in}7\dfrac12 \qquad \textbf{(D)}\hspace{.05in}8 \qquad \textbf{(E)}\hspace{.05in}9$

Solution

Solution 1

Since Rachelle uses $3$ pounds of meat to make $8$ hamburgers, she uses $\frac{3}{8}$ pounds of meat to make one hamburger. She'll need 24 times that amount of meat for 24 hamburgers, or $\frac{3}{8} \cdot 24 = \boxed{\textbf{(E)}\ 9}$ .

Solution 2

Rachelle uses meat for hamburgers in the ratio $\frac{3\text{ lb}}{8\text{ hamburgers}}$ . If we multiply this ratio on top and bottom by 3 to get 24 hamburgers on the bottom, we get $\frac{3\text{ lb}\cdot 3}{8\text{ hamburgers}\cdot 3} = \frac{9\text{ lb}}{24\text{ hamburgers}}$ . Therefore, she uses 9 pounds of meat for 24 hamburgers, making the answer $\boxed{\textbf{(E)}\ 9}$ .

2012 AMC 8 (Problems • Answer Key • Resources)
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All AJHSME/AMC 8 Problems and Solutions

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2012 AMC 8 Problems/Problem 1

Contents

Problem

Solution

Solution 1

Solution 2

See Also