Ms Lane had some money. She spent $x and gave 2/5 of the remainder to her mother. The amount she had left was $240. How much did she have at first if the amount she had left is half of the amount she spent?

Answer 1

Let's break down the problem step by step:

1. Ms Lane spent $x.
2. After spending $x, she had 240 dollars left.
3. This 240 dollars is also half of the amount she spent (x).
4. After spending x dollars, she gave 2/5 of the remaining amount to her mother. This means she kept 3/5 of the remaining amount.
5. If 240 dollars is 3/5 of the remaining amount after spending x dollars, then 1/5 of the remaining amount is 240/3 = 80 dollars.
6. Therefore, the remaining amount after spending x dollars is 4 * 80 = 320 dollars.

Based on this information, we can create the following equation:
x + 240 + 320 = initial amount
x + 560 = initial amount

Since the initial amount is double the amount left after spending x dollars, we can write:
initial amount = 2*(x+240)

Now we can set these two equations equal to each other and solve for x:

2*(x+240) = x + 560
2x + 480 = x + 560
2x - x = 560 - 480
x = 80

Therefore, Ms Lane initially had 80 + 240 + 320 = 640 dollars.