A young man spent 1/4 of his allowance on a movie. He spent 11/18 of the remainder on after-school snacks. Then from the money remaining, he spent $3.00 on a magazine, which left him 1/24 of his original allowance to put into savings. How much of his allowance did he save?
allowance not spent=savings
(A - 1/4 A)(1-11/18)-3=1/24 A
check my thinking.
To find out how much of his allowance the young man saved, we need to follow these steps:
Step 1: Calculate how much money he spent on the movie.
He spent 1/4 of his allowance on a movie, so we can represent it as: 1/4 × (original allowance).
Step 2: Calculate how much money he had left after spending on a movie.
To find the remainder, we subtract the amount spent on the movie from the original allowance: (original allowance) - (1/4 × original allowance).
Step 3: Calculate how much money he spent on after-school snacks.
He spent 11/18 of the remainder on snacks, so we can represent it as: 11/18 × (remaining allowance after movie).
Step 4: Calculate how much money he had left after spending on snacks.
To find the remainder, we subtract the amount spent on snacks from the remaining allowance: (remaining allowance after movie) - (11/18 × remaining allowance after movie).
Step 5: Calculate how much money he spent on a magazine.
He spent $3.00 on a magazine, so we subtract $3.00 from the remaining allowance.
Step 6: Calculate how much money he had left to put into savings.
To find the amount left for savings, we subtract the magazine expense from the remaining allowance: (remaining allowance after snacks) - $3.00.
Step 7: Find the fraction of the original allowance that he saved.
The remaining allowance for savings represents 1/24 of his original allowance.
Answer: He saved 1/24 of his original allowance.
Let's calculate step by step:
1. The young man spent 1/4 of his allowance on a movie.
Total allowance spent on the movie = (1/4) x Total allowance
2. After spending on the movie, he had a remainder.
Remainder = Total allowance - Total allowance spent on the movie
3. He spent 11/18 of the remainder on after-school snacks.
Total spent on snacks = (11/18) x Remainder
4. After spending on snacks, he had a remaining amount.
Remaining amount = Remainder - Total spent on snacks
5. He spent $3.00 on a magazine from the remaining amount.
Remaining amount after buying a magazine = Remaining amount - $3.00
6. The remaining amount after buying a magazine is 1/24 of his original allowance.
Remaining amount after buying a magazine = (1/24) x Total allowance
Now we can set up an equation to solve for the remaining amount:
Remaining amount after buying a magazine = (1/24) x Total allowance
Remaining amount - $3.00 = (1/24) x Total allowance
Substituting the value of the remaining amount:
(Remainder - $3.00) = (1/24) x Total allowance
Simplifying the equation:
Remainder = (1/24) x Total allowance + $3.00
Since we want to find out how much he saved, the remaining amount in step 6 is the saved amount.
Therefore, the amount he saved = Remaining amount after buying a magazine.