Jake spent 3/8 of his money on a book and 1/2 of what was left on a magazine. He now has $6.25. How much money did he start with?
To solve this problem, let's work backward. We know that Jake has $6.25 left after spending some of his money.
Let's say he spent x dollars on the magazine. We also know that he spent 1/2 of what was left after buying the book. Therefore, the amount of money he had after buying the book can be calculated as 2 * (6.25 + x).
Now, we know that the money he had after buying the book is 3/8 of his total money. So we can write the equation:
2 * (6.25 + x) = (3/8) * total money.
To find the total money, we need to solve this equation.
First, simplify the equation:
12.5 + 2x = (3/8) * total money.
Next, isolate the total money on one side of the equation:
(3/8) * total money = 12.5 + 2x.
Multiply both sides of the equation by (8/3) to get rid of the fraction:
total money = (8/3) * (12.5 + 2x).
Now, substitute the value of total money with $6.25 in the equation:
6.25 = (8/3) * (12.5 + 2x).
Multiply both sides of the equation by (3/8):
(3/8) * 6.25 = 12.5 + 2x.
Simplify:
2.34375 = 12.5 + 2x.
Subtract 12.5 from both sides of the equation:
2x = -10.15625.
Finally, divide both sides of the equation by 2 to find the value of x, which represents the money spent on the magazine:
x = -5.078125.
Since money cannot be negative, this implies that our calculations are incorrect. Please double-check the information provided in the problem.