An Antique dealer visited three shops. she spend $25 at the first shop. At the second shop, she spent half of her remaining money. At the third shop, she spent one third of her remaining money and had $60 left. How much money did the dealer have orginally?
To find out how much money the dealer originally had, we can work backwards by adding the amounts spent at each shop.
Let's denote the original amount of money the dealer had as "x".
1. At the first shop, the dealer spent $25, which means she had x - $25 left.
2. At the second shop, she spent half of her remaining money, so she spent (1/2)(x - $25). Thus, she had (x - $25) - (1/2)(x - $25) = (1/2)(x - $25) left.
3. At the third shop, she spent one third of her remaining money, so she spent (1/3)[(1/2)(x - $25)]. Consequently, she had (1/2)(x - $25) - (1/3)[(1/2)(x - $25)] = (1/3)[(1/2)(x - $25)] left, which amounts to $60.
Now, we can set up the equation and solve for x:
(1/3)[(1/2)(x - $25)] = $60
To simplify, we can multiply both sides of the equation by 6 to get rid of the denominators:
[(1/2)(x - $25)] = $60 * 6
(x - $25) = $360
x = $360 + $25
x = $385
Therefore, the dealer originally had $385.