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?
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Let x = amt originally in the bowl
:
"Ellen takes 1/4 of the oranges in a bowl"
x - {{{1/4}}}x = {{{3/4}}}x remaining
;
Jeff takes 1/3 of the remaining oranges in the bowl.
that means he leaves 2/3
{{{2/3}}} * {{{3/4}}}x = {{{6/12}}}x
{{{6/12}}}x reduces to {{{1/2}}}x remaining
:
Ellen and Jeff later decide that they don't need all their oranges so they each put 1 back in the bowl.
{{{1/2}}}x + 2
:
Carlos takes 1/2 of the oranges that remain in the bowl There are now 4 oranges left in the bowl.
{{{1/2}}}({{{1/2}}}x + 2) = 4
multiply both sides by 2
{{{1/2}}}x + 2 = 8
{{{1/2}}}x = 8 - 2
{{{1/2}}}x = 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