Alicia went shopping and spent 1/3 of her money on a table. She spent 1/4 of it.on a sofa. She then spent 1/2 of the remainder on a chair and another $52 on a lamp. Given that she had 1/8 of her money left, how much did she
spend on the table?
To find out how much Alicia spent on the table, let's break down the problem step by step.
Step 1: Calculate the amount Alicia had left after buying the lamp.
We are given that when Alicia had finished shopping, she had 1/8 of her money left. So, we can assume that the money left is 1 part out of 8. Let's represent the total amount of money Alicia started with as "M". After buying the lamp, she had 1/8 of her money left, which is (1/8) * M.
Step 2: Calculate the amount Alicia spent on the chair.
We know that Alicia spent 1/2 of the remaining money on a chair. So, the amount spent on the chair is (1/2) * [(1/8) * M].
Step 3: Calculate the amount Alicia spent on the sofa.
Alicia spent 1/4 of her money on a sofa, that is (1/4) * M.
Step 4: Calculate the amount Alicia spent on the table.
Now, we need to find the amount Alicia spent on the table. We already know the amounts spent on the chair and the sofa, so we can find the remaining amount by subtracting the sum of those two amounts from the initial amount of money Alicia had.
Remaining amount = M - [(1/8) * M + (1/2) * (1/8) * M + (1/4) * M]
Step 5: Simplify the equation.
Simplifying the equation, we get:
Remaining amount = M - [(1/8) * M + (1/16) * M + (1/4) * M]
Remaining amount = M - [(2/16) * M + (1/16) * M + (4/16) * M]
Remaining amount = M - [(7/16) * M]
Step 6: Set up the equation using the given information.
We are also given that Alicia spent $52 on the lamp. So, the remaining amount after buying the lamp is:
Remaining amount - $52 = (1/8) * M
Step 7: Solve the equation.
Let's plug in the remaining amount and solve for M:
(M - (7/16) * M) - $52 = (1/8) * M
(16/16) * M - (7/16) * M = (1/8) * M + $52
(9/16) * M = (1/8) * M + $52
Now, let's solve for M:
(9/16) * M - (1/8) * M = $52
[(9/16) - (1/8)] * M = $52
[(9 - 2)/16] * M = $52
(7/16) * M = $52
To isolate M, we'll multiply both sides by (16/7):
(7/16) * M * (16/7) = $52 * (16/7)
M = $832/7
M = $118.86 (rounded to the nearest cent)
Step 8: Calculate the amount spent on the table.
We already know the remaining amount after buying the lamp is (1/8) * M, which is $118.86 * (1/8).
Amount spent on the table = $118.86 - ($118.86 * (1/8))
Amount spent on the table = $118.86 - $14.86
Amount spent on the table = $104.00
Therefore, Alicia spent $104.00 on the table.