An antique dealer visited three shops. She spent $25 at the first shop. At the second shop, she spent half of her remaining money and had $60 left. How much money did the dealer have originally.
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To find out how much money the antique dealer had originally, let's break down the given information step by step:
1. The dealer spent $25 at the first shop.
2. At the second shop, she spent half of her remaining money and had $60 left.
Let's assume the amount of money the dealer originally had is represented by the variable 'x'.
1. The dealer spent $25 at the first shop, so the amount of money remaining after this expenditure is x - $25.
2. At the second shop, she spent half of her remaining money. Therefore, the amount she spent at the second shop is (1/2)(x - $25).
3. After spending half of her remaining money at the second shop, the dealer had $60 left. So we can set up the equation: (x - $25) - (1/2)(x - $25) = $60.
Let's solve the equation to determine the value of x:
(x - $25) - (1/2)(x - $25) = $60
Multiplying 1/2 inside the brackets:
x - $25 - (1/2)x + $12.50 = $60
Combining like terms:
(1/2)x - $12.50 = $60
Adding $12.50 to both sides:
(1/2)x = $60 + $12.50
(1/2)x = $72.50
Multiplying both sides by 2 (to isolate x):
x = 2($72.50)
x = $145
Therefore, the dealer originally had $145.