how do solve this question?
jane budgets her monthly take-home pay. the remainder she deposits in her savings account . she budgets 1/3 of her take-home pay for rent, 1/8 for car expenses,1/6 for food , 1/24 for insurance and 1/16 for entertainment. what is jane's monthly take-home pay if she deposits $546 in her savings account?
48 is your common denominator.
16/48=rent, 6/48=car, 8/48=food, 2/48=insurance, 3/48=entertainment. Add them all up and she spends 35/48 of her money. She saves 13/48 of her money. 13/48 of $546 = ? That is your answer
To solve this question, we need to find the total amount of Jane's monthly take-home pay.
Let's assign a variable to Jane's take-home pay, such as "T".
According to the information given, Jane budgets 1/3 of her take-home pay for rent, which can be written as (1/3)T.
Similarly, Jane budgets 1/8 of her take-home pay for car expenses, which can be written as (1/8)T.
Jane budgets 1/6 of her take-home pay for food, which can be written as (1/6)T.
She budgets 1/24 of her take-home pay for insurance, which can be written as (1/24)T.
Finally, she budgets 1/16 of her take-home pay for entertainment, which can be written as (1/16)T.
To find the remaining amount that Jane deposits in her savings account, we subtract the sum of the budgeted amounts from her take-home pay:
T - [(1/3)T + (1/8)T + (1/6)T + (1/24)T + (1/16)T] = $546
Now, let's solve this equation:
T - [(8/24)T + (3/24)T + (4/24)T + (1/24)T + (3/24)T] = $546
T - (19/24)T = $546
(5/24)T = $546
Multiplying both sides of the equation by (24/5) to isolate T, we get:
T = $546 * (24/5)
T = $2,609.6
Therefore, Jane's monthly take-home pay is $2,609.6.