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?
please help me i am confused...
thank you :)
after spending 3/8 of $x he has 5x/8 left
then he spends 1/2 of that, leaving
5x/16
5x/16 = 6.25
5x = 100
x = 20
check: 3/8 of 20 = 7.5
leaving him with 20-7.5 = 12.50
1/2 of that is 6.25, leaving him with 6.25, Check!
To start solving this problem, we need to break it down into step-by-step calculations and equations.
Let's assume that Jake started with X amount of money.
Step 1: Jake spent 3/8 of his money on a book.
This means he spent (3/8) * X on the book. Now he has (X - (3/8) * X) = (5/8) * X left.
Step 2: Jake then spent 1/2 of what was left on a magazine.
So, he spent (1/2) * (5/8) * X on the magazine. Now he has (5/8) * X - (1/2) * (5/8) * X left.
Step 3: According to the problem, Jake now has $6.25.
So, we can set up an equation:
(5/8) * X - (1/2) * (5/8) * X = $6.25
Step 4: Simplify the equation and solve for X.
Multiply both sides of the equation by the common denominator (8) to eliminate the fractions:
5X - 5/2 * X = $6.25 * 8
10X - 5X/2 = $50
Multiply through by 2 to eliminate the fraction:
20X - 5X = $100
15X = $100
Now, divide both sides by 15 to solve for X:
X = $100 / 15
Therefore, Jake started with $100 / 15 = $6.67.