Question 1201639: Hi
Kaden and Dan had a total of $240 . Kaden gave 1/5 to Dan. As a result both had the same amount of money in the end. How much did Dan have at first.
Thanks
PS my son couldn't solve this problem. Ie no solution
Found 5 solutions by greenestamps, mananth, josgarithmetic, ikleyn, MathTherapy:
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
The problem is poorly written, as you show it.
"Kaden gave 1/5 to Dan."
1/5 of a dollar?
1/5 of his money?
1/5 of the total $240?
1/5 of a sandwich?
If you have posted the problem exactly as given to you, then you/I have to guess the meaning; I can't help.
Or if you haven't shown the whole problem, then re-post, showing the problem exactly as it was given to you.
Answer by mananth(16946)  (Show Source):
You can put this solution on YOUR website! Kaden and Dan had a total of $240 . Kaden gave 1/5 to Dan. As a result both had the same amount of money in the end. How much did Dan have at first.
Let Kaden have $x then Don will have the balance (240-x)
Kaden gave 1/5 to Dan.(1/5 x)
So Kaden has (4/5)x
Don will have (240-x) + (1/5) x
=240-(4/5)x
They both had same amount after sharing
(4/5)x = 240-(4/5)x
(8/5)x =240
8x = 5*240
x = 5*240/8
x =150
Kaden has $150
Don has $90
Answer by josgarithmetic(39617)  (Show Source):
Answer by ikleyn(52781)  (Show Source):
You can put this solution on YOUR website! .
Kaden and Dan had a total of $240 . Kaden gave 1/5 to Dan.
As a result both had the same amount of money in the end. How much did Dan have at first.
~~~~~~~~~~~~~~~~~~
There is simple and elegant mental solution.
At final, Kaden and Dan have the same amount of 240 dollars: the total does not change, right?
And at final, they have equal amounts, righ?
Hence, at the end each of them has 120 dollars.
Next, Kaden's final amount of 120 dollars is 4/5 of what Kaden had initially.
It implies that 1/5 of what Kaden had initially is 120/4 = 30 dollars.
Hence, the amount which Kaden had initially, was 5*30 = 150 dollars,
and the amount which Dan had initially, was 240 - 150 = 90 dollars.
At this point, the problem is just solved.
ANSWER, Initially, Dan had $90.
Solved (mentally).
My interior voice tells me that this mental solution is what is expected.
Answer by MathTherapy(10552)  (Show Source):
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