Edna spent 4/13 of her weekly allowance on snacks, 2/7 of the remainder on books and 1/8 of what remained on transportation. If she still had $100, how much was her weekly allowance
total allowance ---- x
amount left after getting snacks = (9/13)(x) = 9x/13
amount left after buying books = (5/7)(9x/13) = 45x/91
amount left after transportation = (7/8)(45x/91) = 45x/104
then 45x/104 = 100
45x = 10400
x = 231.11
Her allowance was 231.11
check:
she spent 4/13 of 231.11 or 71.11 on snacks, leaving her with160
she spent 2/7 of 160 on books, or 45.714, leaving her with 114.2857
she spent 1/8 of 114.2857 on transp, or 14.2857, leaving her with 100.00
my answer is correct.
To find out Edna's weekly allowance, we can work backward through the expenses:
Let's start with her remaining amount after spending 4/13 on snacks. We can calculate this by subtracting 4/13 from 1 (representing the total amount), and then multiplying the result by her total allowance:
Remaining after snacks: (1 - 4/13) * Total allowance
Next, we can find the amount she spent on books. We multiply the remaining amount from the previous step by 2/7:
Spent on books: Remaining after snacks * 2/7
Then, we calculate the amount remaining after books:
Remaining after books: Remaining after snacks - Spent on books
Finally, we can calculate the remaining amount after transportation. We multiply the remaining amount from the previous step by 1/8:
Remaining after transportation: Remaining after books * 1/8
According to the problem, Edna still has $100 remaining. Therefore, we can set up the following equation:
Remaining after transportation = $100
Now we can solve for the total allowance:
(1 - 4/13) * Total allowance - (Remaining after snacks * 2/7) - (Remaining after books * 1/8) = $100
Simplifying this equation will allow us to find the value of Edna's total weekly allowance.
Let's break down the problem step by step.
Step 1: Calculate the amount Edna spent on snacks.
Edna spent 4/13 of her weekly allowance on snacks. So, if we let x be her weekly allowance, she spent (4/13) * x on snacks.
Step 2: Calculate the amount Edna had remaining after spending on snacks.
The remainder after spending on snacks would be the total allowance minus the amount spent on snacks.
Remainder = x - (4/13) * x
Step 3: Calculate the amount Edna spent on books.
Edna spent 2/7 of the remainder on books. So, she spent (2/7) * (x - (4/13) * x) on books.
Step 4: Calculate the amount Edna had remaining after spending on books.
The remainder after spending on books would be the previous remainder minus the amount spent on books.
Remainder = (x - (4/13) * x) - (2/7) * (x - (4/13) * x)
Step 5: Calculate the amount Edna spent on transportation.
Edna spent 1/8 of what remained on transportation. So, she spent (1/8) * [(x - (4/13) * x) - (2/7) * (x - (4/13) * x)] on transportation.
Step 6: Calculate the final amount Edna had.
The final amount Edna had would be the previous remainder minus the amount spent on transportation, which is $100.
Remainder = [(x - (4/13) * x) - (2/7) * (x - (4/13) * x)] - (1/8) * [(x - (4/13) * x) - (2/7) * (x - (4/13) * x)]
Step 7: Solve for x.
We have the equation: [(x - (4/13) * x) - (2/7) * (x - (4/13) * x)] - (1/8) * [(x - (4/13) * x) - (2/7) * (x - (4/13) * x)] = 100.
Now, you can solve this equation to find the value of x, which represents Edna's weekly allowance.