1999 AMC 8 Problems/Problem 22

Problem

In a far-off land three fish can be traded for two loaves of bread and a loaf of bread can be traded for four bags of rice. How many bags of rice is one fish worth?

$\text{(A)}\ \frac{3}{8} \qquad \text{(B)}\ \frac{1}{2} \qquad \text{(C)}\ \frac{3}{4} \qquad \text{(D)}\ 2\frac{2}{3} \qquad \text{(E)}\ 3\frac{1}{3}$

Solution

Let $f$ represent one fish, $l$ a loaf of bread, and $r$ a bag of rice. Then: $3f=2l$ , $l=4r$

Substituting $l$ from the second equation back into the first gives us $3f=8r$ . So each fish is worth $\frac{8}{3}$ bags of rice, or $2 \frac{2}{3}\Rightarrow \boxed{D}$ .

1999 AMC 8 (Problems • Answer Key • Resources)
Preceded by Problem 21	Followed by Problem 23
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1999 AMC 8 Problems/Problem 22

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