# A tiny statue of Tom Brady is 2 8/15 inches tall If the statue uses a scale of 1 inch 2.5 feet, what is Tom Brady's actual height?

Aug 14, 2017

$6$ feet and $4$ inches

#### Explanation:

First, we can set up a proportion.

$\left(2 \frac{8}{15} \textcolor{w h i t e}{i} \text{in")/ (color(red)x color(white)i "ft") = (1 color(white)i "in") / (2.5 color(white)i "ft}\right)$

Now we can cross-multiply and solve for $\textcolor{red}{x}$.

$2 \frac{8}{15} \cdot 2.5 = 1 \textcolor{red}{x}$

$\frac{38}{15} \cdot 2.5 = \textcolor{red}{x}$ $\to$ rewrite the mixed number as an improper fraction

$\frac{38}{15} \cdot \frac{5}{2} = \textcolor{red}{x}$ $\to$rewrite the decimal as an improper fraction

${\cancel{38}}^{19} / {\cancel{15}}^{3} \cdot {\cancel{5}}^{1} / {\cancel{2}}^{1} = \textcolor{red}{x}$ $\to$ cancel

$\textcolor{red}{x} = \frac{19}{3}$

$\textcolor{red}{x} = 6 \frac{1}{3}$ $\to$rewrite improper fraction as a mixed number

Tom Brady's height is $6 \frac{1}{3} \textcolor{w h i t e}{i} \text{ft}$, but it would make more sense to write his height using feet and inches.

$\frac{1}{3}$ of $1 \textcolor{w h i t e}{i} \text{ft" = 1/3 * 12 color(white)i "in" = 4 color(white)i "in}$

So, Brady's actual height is $6 ' 4 ' '$ or $6$ feet and $4$ inches.