Joe spent 25% of his money on food. He spent 25% of the remainder on drink. He had $9 left. How much money did Joe have to start?
.25 x for food
.25 * .75 x for drink = .1875 x
.25 x + .1875 x = .4375 x spent
x - .4375 x = 9
.5625 x = 9
x = $ 16
Let's go step by step to solve this problem.
Step 1: Let's assume that Joe had x dollars to start.
Step 2: Joe spent 25% of his money on food, which is 0.25x dollars.
Step 3: After spending on food, Joe had (x - 0.25x) dollars remaining.
Step 4: Now, Joe spent 25% of the remainder on drinks, which is 0.25 * (x - 0.25x) dollars.
Step 5: After spending on drinks, Joe had (x - 0.25x) - 0.25 * (x - 0.25x) dollars remaining.
Step 6: According to the problem, Joe had $9 left, so we can set up the equation as follows:
x - 0.25x - 0.25 * (x - 0.25x) = 9
Step 7: Simplify and solve the equation:
x - 0.25x - 0.25x + 0.0625x = 9
0.5x - 0.0625x = 9
0.4375x = 9
x = 9 / 0.4375
x ≈ 20.571
Therefore, Joe had approximately $20.571 to start with.
To find out how much money Joe had to start with, we can work backward from the given information.
Let's assume that the amount of money Joe initially had is x dollars.
Joe spent 25% of his money on food, which means he spent (25/100) * x dollars on food. This leaves him with the remainder, which is (100 - 25)% = 75% of his initial money.
So, Joe has 75% of x dollars left after spending on food, which is (75/100) * x = (3/4) * x dollars.
Joe then spent 25% of the remainder on drinks, which is (25/100) * (3/4) * x dollars.
We know that Joe had $9 left after spending on drinks, so we can set up the equation:
(25/100) * (3/4) * x = $9
Now, we can solve this equation to find the value of x, which represents the initial amount of money Joe had.
Multiplying the fractions (25/100) * (3/4), we get (25/100) * (3/4) = 3/16.
So, the equation becomes:
(3/16) * x = $9
To isolate x, we can multiply both sides of the equation by 16/3:
x = ($9) * (16/3)
Calculating this, we find:
x ≈ $48
Therefore, Joe had approximately $48 to start with.