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Nate learned to sing a total of $18$ pieces over the course of $9$ weeks of voice lessons. After $10$ weeks of voice lessons, how many pieces will Nate be able to sing, in total? Assume the relationship is directly proportional. $\newline$ _____ pieces

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Solve proportions: word problems

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Q. Nate learned to sing a total of

18

pieces over the course of

9

weeks of voice lessons. After

10

weeks of voice lessons, how many pieces will Nate be able to sing, in total? Assume the relationship is directly proportional.

\newline

_____ pieces

Identify values, set up proportion: Identify the known values and set up the proportion. $\newline$ ● Total pieces learned in $9$ weeks: $18$ pieces $\newline$ ● Total pieces to be learned in $10$ weeks: $x$ pieces $\newline$ Set up the proportion based on the known values. $\newline$ $\frac{18}{9} = \frac{x}{10}$
Cross-multiply to find $x$ : Cross-multiply to find $x$ . $\newline$ Cross-multiplying gives: $\newline$ $18 \times 10 = 9 \times x$ $\newline$ $180 = 9x$
Solve for x: Solve for x. $\newline$ Divide both sides by $9$ to isolate x. $\newline$ $\frac{180}{9} = x$ $\newline$ $20 = x$

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