Xuxian and Rachel had the same number of marbles. After Rachel gave away 22 marbles, Rachel had 3 times as many marbles as Xuxian. How many marbles did each of them have at first

Guest Nov 10, 2014

#2**+8 **

This question makes no sense.....if they both start wiith the same number and Rachel gives 22 of them away, she can't end up with 3 times as many marbles as Xuxian

CPhill
Nov 10, 2014

#4**+3 **

Ah... I see what you mean, happy7.......can you show how you got your answer.....or did you just use logic???

CPhill
Nov 10, 2014

#5**+8 **

I guessed and tested. I knew that they would have to have more than 22 marbles at the start. Then I thought, Maybe I'll start at thirty and work my way up.

30-22=8.

8*3=24.

Too low.

35-22=13

13*3=39

Too high.

Maybe in the middle.

33-22=11

11*3=33

Just right.

And there you have it. The answer

happy7
Nov 10, 2014

#6**+8 **

OK....I used to do that, too!!!.....it can be effective.....but sometimes lengthy....

Let's solve it with some math

Let x be the number they both start with

And when Rachel gives away 22, Xuxian has 3 times as many.

So, at the end, Rachel has x -22 and Xuxian has x + 22

And 3 times the number she has = Xuxian's total......so we have

3(x - 22) = x + 22 simplify

3x - 66 = x + 22 subtract x from both sides

2x - 66 = 22 add 66 to both sides

2x = 88 divide both sides by 2

x = 44 this is what they started with

So, Rachel ends up with 44 - 22 = 22

And Xuxian ends up with 44 + 22 = 66

CPhill
Nov 10, 2014

#7**+8 **

Your answer could be correct... but it didn't say who Rachel gave her marbles to. So I guess we are both right.. or could be right at least... the question isn't specific.

happy7
Nov 10, 2014