Budgets

Explanation

In order to find the fraction of net take-home pay that should be spent on housing, we need to sum up all the fractions spent elsewhere and subtract it from 1.

Start by summing up the fractions with the similar denominators and simplify them if possible

Fractions with denominator 25 = Utilities  + Clothing + Medical = \(\require{cancel}\frac{2}{25} + \frac{1}{25} + \frac{2}{25} = \frac{5}{25} = \frac{5}{5 \cdot 5} = \frac{\cancel{5}^1}{\cancel{5}_1 \cdot 5} = \frac15\) 

Fractions with denominator 20 = Transportation + Savings + Personal = \(\require{cancel} \frac{3}{20} + \frac{1}{20} + \frac{1}{20} = \frac{5}{20} = \frac{5}{4 \cdot 5} = \frac{\cancel{5}^1}{4 \cdot \cancel{5}_1} = \frac14\)

Fractions with denominator 10 = Food + Debt = \(\require{cancel} \frac{1}{10} + \frac{1}{10} = \frac{2}{10} = \frac{2}{2 \cdot 5} = \frac{\cancel{2}^1}{\cancel{2}_1 \cdot 5} = \frac15\)

Now sum all simplified fractions

$\frac15 + \frac14 + \frac15 = \frac14 + \frac25$

Find the LCD which is 20 

$= \frac14 \cdot \frac55 + \frac25 \cdot \frac44$

Add the numerators

$= \frac{5}{20} + \frac{8}{20} = \frac{13}{20}$

So, the take-home pay will be 1 - \(\frac{13}{20}\) or \(\frac{20}{20} - \frac{13}{20}\)

$1 - \frac{13}{20} = \frac{7}{20}$

The fraction of net take-home pay is \(\frac{7}{20}\)