Keith spent 1 5 of his money on a story book he gave $46.80 to his brother and had 1 2 of his money left how much money did he left?
If Keith spent 1/5 of his money on a storybook, then he had 5/5 - 1/5 = <<5/5-1/5=4/5>>4/5 of his money left.
Let M be the amount of money Keith had.
He gave his brother $46.80, so he had 4/5M - $46.80 = 1/2M left.
Thus, 4/5M - 1/2M = $46.80.
Therefore, 4/5M - 2/5M = $46.80.
Thus, 2/5M = $46.80.
Therefore, M = $46.80 / (2/5) = $46.80 / (2/5) = $46.80 / (2/5) = $117.
Thus, Keith had $117 - $46.80 = $<<117-46.80=70.20>>70.20 left. Answer: \boxed{70.20}.
Let's break down the steps to solve this problem:
1. Keith spent 1/5 of his money on a storybook. Let's represent his total money as "M". The amount he spent on the storybook can be calculated as (1/5) * M.
2. Keith gave $46.80 to his brother. This amount should be subtracted from the remaining money after buying the storybook.
3. After giving money to his brother, Keith had 1/2 of his money left. The remaining money can be calculated as (1/2) * (M - (1/5) * M - 46.80).
Let's solve the equation:
Remaining money = (1/2) * (M - (1/5) * M - 46.80)
Simplifying the equation further:
Remaining money = (1/2) * (4/5) * M - (1/2) * 46.80
Multiplying and simplifying:
Remaining money = (2/5) * M - 23.40
So, the expression for Keith's remaining money is (2/5) * M - 23.40. Without knowing the value of M, we cannot determine the exact amount of money Keith has left.
To find the amount of money Keith had left after buying a story book and giving some money to his brother, we will need to use some calculations.
Let's assume that Keith had "x" amount of money initially.
According to the given information:
- He spent 1/5 of his money on a story book. Therefore, he spent (1/5) * x = x/5 on the story book.
- Then, he gave $46.80 to his brother.
- After giving money to his brother, he had 1/2 of his money left. Therefore, he had (1/2) * x = x/2 remaining.
To find the amount of money Keith had left, we need to subtract the amount spent on the story book and the money given to his brother from the initial amount of money.
x - (x/5) - $46.80 = x/2
To simplify the equation, we can multiply both sides by 10 to eliminate the fractions:
10x - 2x - 468 = 5x
Next, we can combine like terms:
8x - 468 = 5x
To isolate the variable, we'll subtract 5x from both sides:
8x - 5x - 468 = 0
Simplifying further:
3x - 468 = 0
Now, we'll add 468 to both sides:
3x = 468
Finally, divide both sides by 3 to solve for x:
x = 468 / 3
x = 156
Therefore, Keith initially had $156. After deducting the amount spent on the story book and the money given to his brother, he had (1/2) * $156 = $78 left.