math
posted by Ire on .
Jack and Jill got an equal number of marbles from their grandpa's collection. Jill gave 50 marbles to Jack because she saw that he was more interested in marbles than she was. Now Jack has 5 times as many marbles as Jill. How many total marbles did grandpa give away and how many did they each get?

This is a logic problem. I will write out the steps below.
Ja= Jack
Ji= Jill
Jill gives 50 to Jack, so she has 50 less and he has 50 more.
And, this quantity of 50 more is equal to 5 times Jill's amount.
So, now Jill has Ji50 and Jack has Ja + 50
So, now just think how to set this up algebraically: If they both had 100 to start with, and Jill gives away 50, she has 50 now, and Jack has 150. So, the difference between the two will always be 100, no matter what number you choose for the beginning value. So, Jill will have 100 less marbles than Jack now.
Ji= Ja 100
Now we develop a new relationship:
Ja= 5 Ji
Ja= 5 ( Ja  100)
Ja= 5Ja500
Ja + 500= 5Ja
4Ja= 500
Ja= 125
Now solve for Ji using Ja= 5 Ji
125= 5 Ji
J= 25
Now since Jill gave him 50 and he took 50, you subtract 50 from his pile, and add 50 to hers.
So, Jill had 75 to begin with and Jack had 75 to begin with.
Check backwards:
7550= 25= Ji now
75 + 50= 125= Ja now
Is this statement true: Ja= 5 Ji?
125= 5 * 25
125= 125
Yes! It is. So, this is your answer!
Hope this helps! 
This is a question to the answer above
Got it. I was confused with the question because what if they did NOT start with the same amount but did receive same amount from grandpa? Is that a different problem or cannot be done? 
Yoyoma, can you please answer the question on what if Jack & Jill did NOT start with equal amount of marbles?