Alex spent 3/7 of his money. He gave 1/4 of the remainder to his sister. He had 120 left. How much money had he at first?
3/7 spent leaves 4/7
1/4 of 4/7 is 1/7, so 3/7 left
3/7 x = 120
Let's break down the problem step-by-step:
Step 1: Calculate the amount of money Alex had left after spending 3/7 of his money.
Let's assume the amount of money Alex had at first is 'x'.
Amount spent = 3/7 * x
Amount remaining = x - 3/7 * x = 4/7 * x
Step 2: Calculate the amount of money Alex gave to his sister.
Amount given to sister = 1/4 * (4/7 * x) = 1/4 * 4/7 * x = 1/7 * x
Step 3: Calculate the final amount of money Alex had after giving money to his sister.
Final amount remaining = 4/7 * x - 1/7 * x = 3/7 * x
Step 4: According to the problem, Alex had 120 left.
Therefore, 3/7 * x = 120
Step 5: Solve for x (the original amount of money Alex had).
Multiply both sides of the equation by (7/3):
(7/3) * (3/7) * x = (7/3) * 120
x = 7 * 40
x = 280
Therefore, Alex had $280 at first.
To find out how much money Alex initially had, we can follow these steps:
Step 1: Calculate how much money Alex had left after spending 3/7 of his money.
Let's assume the amount of money Alex initially had was x. After spending 3/7 of his money, he had (1 - 3/7) = 4/7 of his money remaining. So, the value of 4/7 of his money is equal to 120.
To find the value of 1/7, we divide 120 by 4:
(4/7) * x = 120
x = (120 * 7) / 4
x = 210
Therefore, Alex initially had 210 units of money.