# math

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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?

• math -

Let x = original money

x - 25 - .5(x-25) - [.5(x-25)]/3 = 60

Solve for x.

• math -

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.

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