John had a sum of money. He spent $132 on a computer software and 3/4 of his
remaining money on 5 indentical books. The amount he had left wa equal to 1/6 of his
money. How much did each book cost?
x - 132 - 3/4 (x-132) = 1/6 x
find x, and then each book cost 1/5 * 3/4 (x-32)
(3/4)(S-132) = 5 B
[(S-132) - 5 B ](1/4] = (1/6) S
3 S - 396 = 20 B
6 S - 792 - 30 B = 4 S
3 S - 396 - 20 B = 0
2 S - 792 - 30 B = 0
6 S - 792 - 40 B = 0
6 S - 2376 - 90 B = 0
- 1584 + 50 B = 0
B = 1584 / 50 = 31.68
To determine the cost of each book, we can break down the given information step by step.
Let's assume John's initial sum of money is represented by 'x'.
First, John spent $132 on a computer software. Therefore, he now has 'x - 132' money remaining.
Next, he spent 3/4 (or 75%) of his remaining money on 5 identical books. This means he spent (3/4) * (x - 132) on books.
So, the amount he had left, which is equal to 1/6 (or 16.67%) of his initial sum of money, is given by (1/6) * x.
Based on the given information, we can set up an equation to solve for x, the initial sum of money:
(1/6) * x = (3/4) * (x - 132)
To solve this equation, we can eliminate the fractions by multiplying both sides by 12 (the least common multiple of 6 and 4):
2x = 9 * (x - 132)
Expanding the right side:
2x = 9x - 1188
By rearranging terms:
9x - 2x = 1188
7x = 1188
Now, we can solve for x:
x = 1188 / 7
x ≈ 169.71
Therefore, John initially had approximately $169.71.
To find the cost of each book, we need to calculate 75% of his remaining money, which is (3/4) * (169.71 - 132):
Cost of each book = (3/4) * (169.71 - 132) / 5
Calculating this expression:
Cost of each book ≈ 4.25
Therefore, each book costs approximately $4.25.