Jerry had some money. He used 1/3 of his money on a basketball and 3/4 of his
remaining money on a tennis racket. He spent another $5 on his lunch and had 1/8 of
the original amount of money left. How much money did Jerry have at first?
Just from the problem, it x is the all money
So, 7/8x = 1/3x + 2/3x * 3/4 + 5
7/8x = 1/3x + 1/2x + 5
21/24x = 8/24x + 12/23x + 5
1/24x = 5
x = 120
Let's solve this step-by-step.
Let's assume Jerry had x amount of money initially.
1. Jerry used 1/3 of his money on a basketball, which means he spent (1/3) * x on the basketball.
After buying the basketball, Jerry has (x - (1/3) * x) money remaining.
2. Jerry then used 3/4 of his remaining money on a tennis racket, which means he spent (3/4) * (x - (1/3) * x) on the tennis racket.
After buying the tennis racket, Jerry has ((x - (1/3) * x) - (3/4) * (x - (1/3) * x)) money remaining.
3. Jerry spent an additional $5 on his lunch, which means he has ((x - (1/3) * x) - (3/4) * (x - (1/3) * x)) - 5 money remaining.
4. Jerry had 1/8 of the original amount of money left, which means ((x - (1/3) * x) - (3/4) * (x - (1/3) * x)) - 5 = (1/8) * x.
Now, let's simplify the equation and solve for x.
((x - (1/3) * x) - (3/4) * (x - (1/3) * x)) - 5 = (1/8) * x
To simplify, we can start by distributing the fractions:
(x - (1/3) * x) - ((3/4) * x - (3/4) * (1/3) * x) - 5 = (1/8) * x
Next, we simplify each term:
(x - (1/3) * x) - ((3/4) * x - (1/4) * x) - 5 = (1/8) * x
Now, we can simplify the equation further:
(x - (1/3) * x - (3/4) * x + (1/4) * x) - 5 = (1/8) * x
Combining like terms:
(x - (10/12) * x) - 5 = (1/8) * x
(12/12 * x - 10/12 * x) - 5 = (1/8) * x
(2/12 * x) - 5 = (1/8) * x
Next, we can clear the fractions by multiplying both sides of the equation by the least common multiple (LCM) of 12 and 8, which is 24:
(2/12 * x) * 24 - 5 * 24 = (1/8 * x) * 24
2 * x * 2 - 120 = 3 * x
4 * x - 120 = 3 * x
4 * x - 3 * x = 120
x = 120
Therefore, Jerry had $120 initially.
To find out how much money Jerry had at first, we can work backwards from the given information. Let's break the problem down step by step:
Step 1: Jerry used 1/3 of his money on a basketball. This means he has 2/3 of his money left.
Step 2: Next, Jerry used 3/4 of his remaining money on a tennis racket. This means he has 1/4 of his money left.
Step 3: Jerry spent another $5 on his lunch. So, the money he has left is now equal to 1/4 - $5.
Step 4: It's stated that Jerry has 1/8 of the original amount of money left. So, we can set up the equation: (1/4 - $5) = 1/8 * Original amount
Now, let's solve the equation to find the original amount of money Jerry had:
1/4 - $5 = 1/8 * Original amount
To simplify the equation, convert the fractions to a common denominator:
8/32 - $5 = 4/32 * Original amount
Simplifying further:
8/32 - $5 = Original amount/8
Next, convert the mixed number to a fraction:
1/8 - $5 = Original amount/8
To simplify the equation, multiply both sides by 8:
8 * (1/8 - $5) = 8 * (Original amount/8)
This simplifies to:
1 - 8 * $5 = Original amount
Subtract 8 * $5 from 1:
1 - 40 = Original amount
Finally, calculate:
Original amount = -39
From the given information, it seems there might be a mistake in the problem's wording or calculations. The result (-39) implies that Jerry had a negative amount of money at first, which doesn't make sense. Please double-check the problem's statement or calculations.