Kristofor spent $104 of his allowance on a bag. He spent 1/3 of the remainder on a book and saved the rest. If he saved 2/7 of his total allowance, what was Kristofor’s allowance at first?
To find out Kristofor's allowance at first, we need to work backwards from the information given.
Let 'x' be the amount of Kristofor's allowance at first.
From the information given, we can deduce the following steps:
1. Kristofor spent $104 on a bag. So, the remainder of his allowance is x - $104.
2. He then spent 1/3 of the remainder on a book. So, the amount he spent on the book is (1/3) * (x - $104).
3. The amount he saved is the remainder minus the amount spent on the book. So, the amount he saved is (x - $104) - [(1/3) * (x - $104)].
4. According to the given information, he saved 2/7 of his total allowance. So, we can write the equation: (x - $104) - [(1/3) * (x - $104)] = (2/7) * x.
Now, we can solve the equation:
(x - $104) - [(1/3) * (x - $104)] = (2/7) * x
Simplify the equation:
(x - $104) - (1/3)x + ($104/3) = (2/7) * x
To get rid of the fractions, we can multiply the entire equation by the least common denominator, which in this case is 21:
21(x - $104) - 21(1/3)x + 21($104/3) = (2/7) * 21x
21x - 21*$104 - 7x + 7*$104 = 6 * 21x
On simplifying, we get:
14x = 7*$104 + 21*$104 - 2*21*$104
14x = $104 * (7 + 21 - 2*21)
14x = $104 * (7 + 21 - 42)
14x = $104 * (28 - 42)
14x = -$1456
Divide both sides by 14:
x = -$1456/14
x = -$104
Since we can't have a negative amount as an allowance, it seems there might be an error in the given information or the calculations. Please double-check the given information and the calculation steps to verify the correctness of the problem.