Math

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Mrs. Lincoln budgets her monthly take-home pay. The remainder she deposits in her savings account. She budgets 1/3 of her take-home pay rent, 1/8 for car expenses, 1/6 for food, 1/24 for insurance and 1/16 for entertainment. What is Mrs. Lincoln's monthly take-home pay if she deposits $546 in her savings account? PLEASE help me and work it out please and thank you

  • Math -

    x - x/3 - x/8 - x/6 -x/24 - x/16 = 546

    Solve for x by multiplying to get rid of the denominators first. Then combine terms.

  • Math -

    x-x/3-x/8-x/6-x/24-x/16=546

    Multiply both sides by 48 to clear fraction

    48x-16x-6x-8x-2x-3x = 26208

    Combine like terms

    13x = 26208

    To find x divide both sides by 13

    x = 2,016

    Mrs. Lincoln monthly take-home is $2,016

  • Inequalities -

    Budgets her monthly take-home. The remainder she deposits in her savings account. she budgets 1/3 rent. 1/8 for car 1/6 food, 1/24 insurance. and 1/16 for entertainment, What is her monthly take-home pay if she deposits $546.00 in her savings account?

  • Math -

    You want to know what her take-home pay is.

    1/3 goes to rent, 1/8 goes for her car, 1/6 goes to her food, 1/24 goes towards insurance, and 1/16 of the money is for entertainment.

    1/3x represents 1/3 of her unknown amount of take-home payment. 1/8x represents 1/8 of her unknown amount of take-home pay and so on..

    You have to add all the fractions together to find out the total of how much of her payment she spends on all these different activities.

    1/3x+1/8x+1/6x+1/24x+1/16x
    =35/48x

    Now, we know that she spends 35/48 of her take-home pay on her activities.
    She deposits $546.00 to her savings account.

    So,
    35/48x=x-$546
    x represents the take-home pay. 35/48 of x(her take-home payment) is the amount she uses on her activities.
    We have to subtract $546 from x to figure out the amount of money she earns because it tells you how much she deposited.

    35/48x=1x-$546
    -1x -1x
    -13/48x=-$546
    ÷-13/48 ÷-13/48
    x= -$546/1 × -48/13
    x= 26208/13
    x= 2016
    Her monthly take-home pay is $2016.

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