Respuesta :
Answer:
Her monthly income is $4200.
Step-by-step explanation:
Let her monthly income be 'x'.
Given:
Money spent on food and rent = 1/2 of 'x' = [tex]\frac{x}{2}[/tex]
Money spent on clothing = 1/4 of 'x' = [tex]\frac{x}{4}[/tex]
Money spent on entertainment = 1/12 of 'x' = [tex]\frac{x}{12}[/tex]
Money saved = $700
Total money spent = Money on food and rent + Money on clothing + Money on entertainment
Total money spent = [tex]\frac{x}{2}+\frac{x}{4}+\frac{x}{12}[/tex]
Adding by making denominator same. LCD of 2, 4, and 12 is 12. So,
Total money spent is given as:
[tex]Total=\frac{x\times 6}{2\times 6}+\frac{x\times 3}{4\times 3}+\frac{x}{12}\\\\Total=\frac{6x}{12}+\frac{3x}{12}+\frac{x}{12}\\\\Total=\frac{6x+3x+x}{12}\\\\Total = \frac{10x}{12}=\frac{10x\div 2}{12\div 2}=\frac{5x}{6}[/tex]
Now, total money saved is equal to total monthly income minus total money spent. So,
Money saved = Monthly income - Total money spent
[tex]700=x-\frac{5x}{6}\\\\700=\frac{6x}{6}-\frac{5x}{6}\\\\700=\frac{6x-5x}{6}\\\\700=\frac{x}{6}\\\\x=700\times 6=\$4200[/tex]
Therefore, her monthly income is $4200.
