Explain the answer to this riddle please!?

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JohnSe

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Bill buys three items at the store for exactly $100. The second item costs half as much as the first item, and the third item is half as much as the second. How much did each one cost?

First: $57.14, Second: $28.57, Third: $14.29

How did they come across this answer?^
 
x+y+z=100
where x is the first item, y is the second, z is the third.
y costs half as much as x so y=.5x
z costs half as much so z=.5(.5x)=.25x
now plug these back in:
x+.5x+.25x=100
1.75x=100
x=$57.14
Just plug this back in for the values of x, y, z to get the cost of each item.
 
3 items equal 100 dollars so
x + y + z = 100
second is half of first so
y = x/2
third is half the second so
z = y/2 = x/4

so

x +x/2 + x/4 = 100
solve for x

7x/4 = 100

x = 400/7

y = 400 / 14

z = 400 /28
 
3 items equal 100 dollars so
x + y + z = 100
second is half of first so
y = x/2
third is half the second so
z = y/2 = x/4

so

x +x/2 + x/4 = 100
solve for x

7x/4 = 100

x = 400/7

y = 400 / 14

z = 400 /28
 
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