2018 AMC 10A Problems/Problem 8
Joe has a collection of 23 coins, consisting of 5-cent coins, 10-cent coins, and 25-cent coins. He has 3 more 10-cent coins than 5-cent coins, and the total value of his collection is 320 cents. How many more 25-cent coins does Joe have than 5-cent coins?
Solution
Let be the number of 5-cent stamps that Joe has. Therefore, he must have 10-cent stamps and 25-cent stamps. Since the total value of his collection is 320 cents, we can write
$\begin{align*} 5x+10(x+3)+25(23-(x+3)-x)= 320 \\ &\Rightarrow 5x+10(x+3)+25(20-2x)= 320 \\ &\Rightarrow 5x+10x+30+500-50x= 320 \\ &\Rightarrow 35x= 210 \\ &\Rightarrow x= 6 \end{align*}$ (Error compiling LaTeX. ! Package amsmath Error: \begin{align*} allowed only in paragraph mode.)
Joe has 6 5-cent stamps, 9 10-cent stamps, and 8 25-cent stamps. Thus, our answer is
~Nivek
See Also
2018 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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