An antique dealer visited three shops. She spent $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 originally?
started with x
(x - 25) after first shop
(x-25)/2 after second shop
(2/3)(x-25)/2 after third shop
so
(2/6)(x-25) = 60
To solve this problem, let's break it down step by step:
1. Begin with the information given: the dealer spent $25 at the first shop.
2. After spending $25 at the first shop, the dealer then went to the second shop with some remaining money. We need to determine how much money she had left before going to the second shop.
3. At the second shop, the dealer spent half of her remaining money. Let's assume the remaining money is represented by variable X. So, at the second shop, she spent X/2.
4. After spending X/2 at the second shop, she then went to the third shop with some remaining money. We need to determine how much money she had left before going to the third shop.
5. At the third shop, she spent one third of her remaining money. So, we can calculate the amount she spent at the third shop as (1/3) * (X - X/2).
6. According to the problem, after spending at the third shop, she had $60 left. Therefore, we can set up the equation: X - [(X/2) + (1/3)*(X - X/2)] = 60.
7. Now we can solve the equation for X and find the original amount of money the dealer had.
Let's work through the equation to find the value of X:
X - [(X/2) + (1/3)*(X - X/2)] = 60.
Simplifying the equation:
X - [X/2 + (X/3 - X/6)] = 60.
X - [X/2 + 2X/6 - X/6] = 60.
X - [3X/6 + 2X/6 - X/6] = 60.
X - 4X/6 = 60.
X - 2X/3 = 60.
Multiply both sides by 3 to eliminate the fraction:
3X - 2X = 180.
X = 180.
Therefore, the original amount of money the dealer had was $180.