Math
posted by Sadie .
Mrs. Lincoln budgets her monthly takehome pay. The remainder she deposits in her savings account. She budgets 1/3 of her takehome 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 takehome pay if she deposits $546 in her savings account? PLEASE help me and work it out please and thank you

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. 
xx/3x/8x/6x/24x/16=546
Multiply both sides by 48 to clear fraction
48x16x6x8x2x3x = 26208
Combine like terms
13x = 26208
To find x divide both sides by 13
x = 2,016
Mrs. Lincoln monthly takehome is $2,016 
Budgets her monthly takehome. 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 takehome pay if she deposits $546.00 in her savings account?

You want to know what her takehome 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 takehome payment. 1/8x represents 1/8 of her unknown amount of takehome 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 takehome pay on her activities.
She deposits $546.00 to her savings account.
So,
35/48x=x$546
x represents the takehome pay. 35/48 of x(her takehome 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 takehome pay is $2016.