Q. 5 QC - Algebra 1

Question

DRAWING Rosie is making a scale drawing. She is using the scale $\mathbf{1}\mathbf{ }\mathbf{inch}\mathbf{=}\mathbf{3}\mathbf{ }\mathbf{feet}$. How many inches will represent 10 feet?

Step-by-Step Solution

Answer

$\frac{10}{3}$ inches will represent 10 feet.

Step 1. Write a proportion.

Let $l$ be the length in inches, such that,

$\frac{1}{3}=\frac{l}{10}$

Step 2. Means-Extremes Property of proportion

If $\frac{p}{q}=\frac{r}{s}$ and $q,s\ne 0$ then $ps=qr$.

Step 3. Cross product.

Find the cross products.

$\begin{array}{c}1\left(10\right)=3\left(l\right)\\ 10=3l\end{array}$

Step 4. Divide.

Divide each side of the obtained equation by 3.

$\begin{array}{c}\frac{10}{3}=\frac{3l}{3}\\ l=\frac{10}{3}\end{array}$

Therefore, the $\frac{10}{3}$ inches will represent 10 feet.