# Mattie's house consists of two stories and an attic. The first floor is 8 5/6 feet tall, the second floor is 8 1/2 feet tall, and the entire house is 24 1/3 feet tall. How tall is the attic?

Mar 28, 2018

The attic is $7$ feet tall

#### Explanation:

So the total house height is the first floor plus the second floor plus the attic

${H}_{T} = {F}_{1} + {F}_{2} + A$

$A = {H}_{T} - {F}_{1} - {F}_{2}$

where ${H}_{T} = 24 \frac{1}{3}$ or $\frac{73}{3}$

$\textcolor{w h i t e}{w h e r e}$ ${F}_{1} = \textcolor{w h i t e}{/} 8 \frac{5}{6}$ or $\frac{53}{6}$

$\textcolor{w h i t e}{w h e r e}$ ${F}_{2} = \textcolor{w h i t e}{/} 8 \frac{1}{2}$ or $\frac{17}{2}$

SOLVE

$A = \frac{73}{3} - \frac{53}{6} - \frac{17}{2}$

common denominator

$A = \frac{2}{2} \times \frac{73}{3} - \frac{53}{6} - \frac{17}{2} \times \frac{3}{3}$

$A = \frac{146}{6} - \frac{53}{6} - \frac{51}{6}$

$A = \frac{146 - 53 - 51}{6}$

$A = \frac{42}{6}$

$A = 7$

To check our work , ${F}_{1} + {F}_{2} + A$ should equal $\frac{146}{6}$

$\frac{53}{6} + \frac{17}{2} + 7$

common denominator

$\frac{53}{6} + \frac{17}{2} \times \frac{3}{3} + 7 \times \frac{6}{6}$

$\frac{53}{6} + \frac{51}{6} + \frac{42}{6}$

$\frac{53 + 51 + 42}{6}$

$\frac{146}{6}$

Yep, we were right. So the attic is $7$ feet tall