SOLUTION: Ellen takes 1/4 of the oranges in a bowl Jeff takes 1/3 of the remaining oranges in the bowl. Ellen and Jeff later decide that they don't need all their oranges so they each put 1

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Question 213844: Ellen takes 1/4 of the oranges in a bowl Jeff takes 1/3 of the remaining oranges in the bowl. Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl. Carlos takes 1/2 of the oranges that remain in the bowl There are now 4 oranges left in the bowl. How many oranges were originally in the bowl?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Ellen takes 1/4 of the oranges in a bowl Jeff takes 1/3 of the remaining oranges in the bowl.
Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl.
Carlos takes 1/2 of the oranges that remain in the bowl.
There are now 4 oranges left in the bowl.
How many oranges were originally in the bowl?
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Let x = amt originally in the bowl
:
"Ellen takes 1/4 of the oranges in a bowl"
x - 1%2F4x = 3%2F4x remaining
;
Jeff takes 1/3 of the remaining oranges in the bowl.
that means he leaves 2/3
2%2F3 * 3%2F4x = 6%2F12x
6%2F12x reduces to 1%2F2x remaining
:
Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl.
1%2F2x + 2
:
Carlos takes 1/2 of the oranges that remain in the bowl There are now 4 oranges left in the bowl.
1%2F2(1%2F2x + 2) = 4
multiply both sides by 2
1%2F2x + 2 = 8
1%2F2x = 8 - 2
1%2F2x = 6
multiply both sides by 2
x = 2(6)
x = 12 oranges originally
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Check solution:
Ellen takes 1/4 of the oranges in a bowl
1/4 of 12 = 3, leaving 9
Jeff takes 1/3 of the remaining oranges in the bowl.
1/3 of 9 = 3. leaving 6
Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl.
6 + 2 = 8
Carlos takes 1/2 of the oranges that remain in the bowl.
half of 8 = 4