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 monry did he havr left?
Let X be the money Keith had.
Keith spent X/5 on a story book.
Keith gave $46.80.
Keith had X - X/5 - $46.80 = X/2 left.
Multiplying both sides by 10 gives 10X - 2X - 468 = 5X.
Combining like terms gives 3X - 468 = 0.
Adding 468 to both sides gives 3X = 468.
Dividing both sides by 3 gives X = 156.
Thus, Keith had $156/2 = $<<156/2=78>>78 left. Answer: \boxed{78}.
Let's solve the problem step by step:
Step 1: Calculate the money Keith spent on the storybook.
Keith spent 1/5 of his money on the storybook. Let's represent his total money as M. Therefore, the money spent on the storybook is (1/5) * M.
Step 2: Calculate the money Keith gave to his brother.
Keith gave $46.80 to his brother.
Step 3: Calculate the money Keith had left.
Keith had 1/2 of his money left. Using the formula, the money left is (1/2) * M.
Step 4: Set up an equation using the given information.
The total money Keith had can be represented as the sum of the money spent on the storybook, the money given to his brother, and the money left.
(1/5)*M + $46.80 + (1/2)*M = M
Step 5: Solve the equation for M.
To solve for M, we need to get rid of the fractions:
Multiply both sides of the equation by 10 to eliminate the denominator:
2M + 468 + 5M = 10M
Simplify the equation:
7M + 468 = 10M
Subtract 7M from both sides:
468 = 3M
Divide both sides by 3 to solve for M:
M = 156
Step 6: Calculate the money left.
Substitute the value of M into the expression for the money left:
(1/2) * M = (1/2) * 156 = $78
Therefore, Keith had $78 left.
To find out how much money Keith had left, we need to follow these steps:
Step 1: Calculate the amount of money Keith spent on the story book.
We know that Keith spent 1/5 of his money on the story book. So, let's represent Keith's total money as "𝑀".
The amount spent on the story book can be calculated as: 1/5 * 𝑀
Step 2: Calculate the amount of money Keith gave to his brother.
We are given that Keith gave $46.80 to his brother. Let's represent this amount as "𝐴".
Step 3: Calculate the amount of money Keith had left.
We know that Keith had 1/2 of his money left after giving money to his brother. So, let's represent the money he had left as "𝑋".
The equation to calculate 𝑋 can be written as:
𝑀 - (1/5 * 𝑀) - 𝐴 = 1/2 * 𝑀
Let's solve the equation to find the value of 𝑋, which represents the money Keith had left.
(1 - 1/5) * 𝑀 - 𝐴 = 1/2 * 𝑀
(4/5) * 𝑀 - 𝐴 = 1/2 * 𝑀 [Simplifying (1 - 1/5) = 4/5]
(4/5) * 𝑀 - $46.80 = 1/2 * 𝑀 [Substituting 𝐴 = $46.80]
Now, we can solve for 𝑀:
(4/5) * 𝑀 - $46.80 = (1/2) * 𝑀
Multiply through by 10 (to eliminate fractions) and simplify:
8𝑀 - 468 = 5𝑀
Subtract 5𝑀 from both sides:
8𝑀 - 5𝑀 - 468 = 0
3𝑀 - 468 = 0
Add 468 to both sides:
3𝑀 = 468
Divide both sides by 3:
𝑀 = 156
Now that we know 𝑀 (Keith's total money), let's calculate the money he had left, 𝑋:
𝑋 = 𝑀 - (1/5 * 𝑀) - 𝐴
𝑋 = 156 - (1/5 * 156) - 46.80
Calculating the expression:
𝑋 = 156 - (0.20 * 156) - 46.80
𝑋 = 156 - 31.20 - 46.80
𝑋 = 78 - 46.80
𝑋 = $31.20
Therefore, Keith had $31.20 left.