Maricris spends 1/2 of her monthly income on food and rent, 1/4 of her income on clothing and 1/12 on entertainment. She saves the rest whic

Question

Maricris spends 1/2 of her monthly income on food and rent, 1/4 of her income on clothing and 1/12 on entertainment. She saves the rest which is $700. What is her monthly income?

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Aubrey 3 weeks 2021-09-23T21:30:25+00:00 1 Answer 0

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    2021-09-23T21:31:55+00:00

    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’ = \frac{x}{2}

    Money spent on clothing = 1/4 of ‘x’ = \frac{x}{4}

    Money spent on entertainment = 1/12 of ‘x’ = \frac{x}{12}

    Money saved = $700

    Total money spent = Money on food and rent + Money on clothing + Money on entertainment

    Total money spent = \frac{x}{2}+\frac{x}{4}+\frac{x}{12}

    Adding by making denominator same. LCD of 2, 4, and 12 is 12. So,

    Total money spent is given as:

    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}

    Now, total money saved is equal to total monthly income minus total money spent. So,

    Money saved = Monthly income – Total money spent

    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

    Therefore, her monthly income is $4200.

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