a man purchased 3 item which cost 100 dollars. The second item is half of the first, and the third item is have of the second. How much was each item?

F+ 1/2F+1/4F=100

1.75 FirstCost=100

FirstCost then...100*4/7=400/7=57.14 dollars.

Lets check it.

57.14+ 57.14/2 + 57.14/4 =57.14+28.57+14.29 = 100

To find out how much each item cost, let's break down the problem and solve it step by step.

Let's call the cost of the first item "x" dollars. According to the problem, the second item costs half of the first item and the third item costs half of the second item.

So, the second item would cost (1/2)x dollars, and the third item would cost (1/2)(1/2)x = (1/4)x dollars.

Now, we know that the total cost of all three items is $100. We can write this as an equation:

x + (1/2)x + (1/4)x = 100

Next, we can simplify the equation by combining like terms:

(1 + 1/2 + 1/4)x = 100

To add the fractions on the left side of the equation, we need a common denominator, which is 4. We can rewrite the equation as:

(4/4 + 2/4 + 1/4)x = 100

(7/4)x = 100

Now, we can isolate "x" by multiplying both sides of the equation by the reciprocal of 7/4, which is 4/7:

(4/7)(7/4)x = (4/7)(100)

x = 400/7

Therefore, each item costs (400/7) dollars, which is approximately $57.14.

So, the first item costs $57.14, the second item costs half of that, which is $28.57, and the third item costs half of the second item, which is $14.29.