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Adriana learned to play a total of $4$ pieces over the course of $2$ weeks of piano lessons. After $10$ weeks of piano lessons, how many total pieces will Adriana be able to play? Assume the relationship is directly proportional. $\newline$ _____ pieces

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Solve proportions: word problems

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Q. Adriana learned to play a total of

4

pieces over the course of

2

weeks of piano lessons. After

10

weeks of piano lessons, how many total pieces will Adriana be able to play? Assume the relationship is directly proportional.

\newline

_____ pieces

Identify values, set up proportion: Step $1$ : Identify the known values and set up the proportion. $\newline$ ● Pieces learned in $2$ weeks: $4$ $\newline$ ● Pieces learned in $10$ weeks: $x$ $\newline$ Set up the proportion based on the known values. $\newline$ $\frac{4}{2} = \frac{x}{10}$
Cross-multiply to find equation: Step $2$ : Cross-multiply to find the equation. $\newline$ Cross-multiplying gives: $\newline$ $4 \times 10 = 2 \times x$ $\newline$ Which simplifies to: $\newline$ $40 = 2x$
Solve for x: Step $3$ : Solve for x. $\newline$ Divide both sides by $2$ to isolate x: $\newline$ $\frac{40}{2} = \frac{2x}{2}$ $\newline$ $20 = x$

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