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?
Let x = original money
x - 25 - .5(x-25) - [.5(x-25)]/3 = 60
Solve for x.
Original Amt. = $X.
1. Spent: $25.
Bal. = (X-25).
2. Spent: (X-25)/2.
Bal. = (X-25)/2.
3. Spent: (1/3)(X-25)/2 = (x-25)/6.
Bal. = (X-25)/2 - (x-25)/6,
Bal.=3(X-25)/6 - (X-25)/6 = 2(X-25)/6 =
(X-25)/3.
Bal. = (X-25)/3 = $60.
(X-25)/3 = 60,
Multiply both sides by 3:
X - 25 = 180,
X = 180 + 25 = $205. = Original Amt.
To find out the original amount of money the antique dealer had, we can work backward from the information provided. Let's break down the problem step by step:
1. The antique dealer spent $25 at the first shop.
2. At the second shop, she spent half of her remaining money.
3. At the third shop, she spent one third of her remaining money and had $60 left.
Let's assign a variable to represent the original amount of money the dealer had:
Let "x" be the original amount of money.
Step 1: The dealer spent $25 at the first shop, so she had x - $25 remaining.
Step 2: At the second shop, she spent half of her remaining money, which is (x - $25)/2. Therefore, she had (x - $25)/2 remaining after this.
Step 3: At the third shop, she spent one third of her remaining money and had $60 left. This means, (x - $25)/2 - [(x - $25)/2]/3 = $60.
Now, we can solve this equation to find the value of "x".
(x - $25)/2 - [(x - $25)/2]/3 = $60
To simplify the equation, let's find a common denominator:
(3(x - $25) - (x - $25))/6 = $60
(3x - $75 - x + $25)/6 = $60
(2x - $50)/6 = $60
Multiply both sides of the equation by 6 to eliminate the denominator:
2x - $50 = $360
Add $50 to both sides of the equation:
2x = $360 + $50
2x = $410
Divide both sides of the equation by 2 to solve for "x":
x = $410/2
x = $205
Therefore, the original amount of money the dealer had was $205.