Question 1207698: Hi
Selena and Ella shared a sum of money. When Selena's share increased from 500 to 620 dollars, the amount of Ella's share decreased by 20%. How much was Ella's share at first.
Found 3 solutions by math_tutor2020, mananth, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source):
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Answer: $600
Explanation
500 = Selena's initial amount
x = Ella's initial amount
Selena's amount goes from $500 to $620.
Selena gained $120 since 620-500 = 120.
This must mean Ella lost $120.
Ella's amount goes from x to x-120.
This assumes the overall pot of money stays the same (i.e. no new amount of dollars enter it).
The instructions state that Ella's amount decreased by 20%
So,
20% of x = 120 dollars lost
0.20x = 120
x = 120/0.20
x = 600
Selena and Ella start off with $500 and $600 respectively.
They will end up with 500+120 = 620 and 600-120 = 480 dollars after that $120 goes from Ella to Selena.
The percent decrease from 600 to 480 is (600-480)/600 = 0.20 = 20% decrease to help us confirm the answer is correct.
It might be helpful to make a table
| Start | Finish | | Selena | 500 | 620 | | Ella | 600 | 480 |
Answer by mananth(16946)  (Show Source):
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Let Ella's initial share by E
Selena's initial share is $500, and her new share is $620.
The increase in Selena's share is=> 620−500=120
Ella's share decreased by 20%. (given)
Decrease in Ella's share = increase in Selena's share, = $120.
A 20% decrease in Ella's share equals $120 decrease is =20% of her initial share.
0.20×E=120
E=120/0.20=600
So, Ella's initial share was $600.
Answer by MathTherapy(10555)  (Show Source):
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Hi
Selena and Ella shared a sum of money. When Selena's share increased from 500 to 620 dollars, the amount of Ella's share decreased by 20%. How much was Ella's share at first.
Let Ella's ORIGINAL/Old amount be E
Then Ella's NEW/Altered amount = E - 120
Ella's NEW/Altered amount decreased by 20%, or from 100% to 80% (.8)
We then get: E - 120 = .8E
- 120 = .8E - E
- 120 = - .2E
Original/Old amount Ella had, or 
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