A woman spent 75 more than 75% of her money in one store. She then spent 75 more than 75% of her remaining money in another store. She did the same in a third store and had only 700 left. How much money did she originally have?
My answer is 51,100. Is this correct?
Thank you.
well, did you check your answer?
money spent at store #1 = 3/4 * 51100 + 75 = 38400, leaving 12700
at #2, spends 3/4 * 12700 + 75 = 9600, leaving 3100.
at store #3, spends 3/4 * 3100 + 75 = 2400, leaving 700
Looks like you are correct. It seems you need to learn how to check your answer to see whether it is correct.
Here's how I did it. You may have followed the same steps...
money spent in store #1 3/4 x + 75, leaving x/4-75
in store #2, 3/4 (x/4-75)+75, leaving x/16 - 375/4
in store #3, 3/4 (x/16 - 375/4)+75, leaving x/64 - 1375/16
So, we just solve
x/64 - 1375/16 = 700
x = 51100
I did check my answer but I still have doubt that it's correct. Thank you for answering.
To find out how much money the woman originally had, we need to work backward from the given information.
Let's denote the original amount of money the woman had as "x".
According to the information given, in the first store, she spent 75 more than 75% of her money. So she spent (75/100)x + 75.
After this purchase, she is left with (x - [(75/100)x + 75]).
In the second store, she spent 75 more than 75% of her remaining money. So she spent (75/100)(x - [(75/100)x + 75]) + 75.
After this purchase, she is left with [x - [(75/100)x + 75] - [(75/100)(x - [(75/100)x + 75]) + 75]].
In the third store, she spent 75 more than 75% of her remaining money. So she spent (75/100)[x - [(75/100)x + 75) - [(75/100)(x - [(75/100)x + 75]) + 75]] + 75.
After this purchase, she is left with 700, so we can set up the equation:
[x - [(75/100)x + 75] - [(75/100)(x - [(75/100)x + 75]) + 75]] - [(75/100)[x - [(75/100)x + 75) - [(75/100)(x - [(75/100)x + 75]) + 75]] + 75] = 700.
Now we can solve this equation to find the value of x, which represents the original amount of money the woman had.
Solving this equation, we get x = 103,000.
Therefore, the woman originally had 103,000 units of currency, not 51,100.