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# Noah and Kate are shopping for new guitar strings in a music store. Noah buys 2 packs of strings. Kate buys 2 packs of strings and a music book. The book costs $16. Their total cost is$72. How much is one pack of strings? Solution

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Let $x$ be the cost of one pack of strings.

Noah bought 2 packs of strings so his cost is $2x$ dollars.

Kate bought 2 packs of strings and a music book. The music book costs \$16 so her total cost is $2x+16$ dollars.

Their total cost is $72$ so $2x+(2x+16)=72$. Solve this equation for $x$:

\begin{aligned} 2x+(2x+16)&=72\\ 4x+16&=72&&\text{Combine like terms.}\\ 4x&=56&&\text{Subtract 16 on both sides.}\\ x&=14&&\text{Divide both sides by 4.} \end{aligned}

The cost of one pack of strings is then $\boxed{\14}$.

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