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4-66.

Josie and Jules are building a model car. They find that the real car is $54$ inches tall and $180$ inches long. They decide to make their model $3$ inches tall, but now they are having a disagreement. Josie thinks that their model should be $10$ inches long and Jules thinks it should be $129$ inches long. Help them settle their argument by deciding if either of them is correct. Explain how you know exactly how long their model should be. Set up a proportion

Substitute in the given information.

Multiply both sides by $x$ to get it in the numerator.

Multiply both sides by $180$ to remove the fractions.

Solve for $x$.

Josie is correct.

\begin{align*} \frac{\text{car height}}{\text{car length}} &= \frac{\text{model height}}{\text{model length}}\end{align*}

\begin{align*} \frac{\text{car height}}{\text{car length}} &= \frac{\text{model height}}{\text{model length}} \\[8pt] \frac{54}{180} &= \frac{3}{x} \\\end{align*}

\begin{align*} \frac{\text{car height}}{\text{car length}} &= \frac{\text{model height}}{\text{model length}} \\[8pt] \frac{54}{180} &= \frac{3}{x} \\[8pt] x ( \frac{54}{180}) &= (\frac{3}{x})x \\[8pt] \frac{54x}{180} &= 3 \end{align*}

\begin{align*} \frac{\text{car height}}{\text{car length}} &= \frac{\text{model height}}{\text{model length}} \\[8pt] \frac{54}{180} &= \frac{3}{x} \\[8pt] x ( \frac{54}{180}) &= (\frac{3}{x})x \\[8pt] \frac{54x}{180} &= 3 \\[8pt] 180 (\frac{54x}{80}) &= 3(180) \\[8pt] 54x &= 540 \end{align*}

\begin{align*} \frac{\text{car height}}{\text{car length}} &= \frac{\text{model height}}{\text{model length}} \\[8pt] \frac{54}{180} &= \frac{3}{x} \\[8pt] x(\frac{54}{180}) &= (\frac{3}{x})x \\[8pt] \frac{54x}{180} &= 3 \\[8pt] 180 (\frac{54x}{80}) &= 3(180) \\[8pt] 54x &= 540 \\[8pt] x &= 10 \text{ inches} \end{align*}