SOLUTION: At first, Josh and May had some marbles each. After Josh gave 1/4 of his marbles to May. May had 3 times as many marbles as him. May then gave Josh 12 marbles. In the end, each of

Algebra.Com
Question 1143846: At first, Josh and May had some marbles each. After Josh gave 1/4 of his marbles to May. May had 3 times as many marbles as him. May then gave Josh 12 marbles. In the end, each of them had an equal number of marbles. How many marbles did May have at first? Please help
Found 3 solutions by greenestamps, KMST, ikleyn:
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


I'll help you get started; you should have the experience of doing the work to get the answer yourself.

In the beginning, Josh has j marbles and May has m marbles:
Josh = j;
May = m

Then Josh gives 1/4 of his marbles to May:
Josh = j-(1/4)j = (3/4)j;
May = m+(1/4)j

At this point, May has 3 times as many marbles as Josh:
(1)

Next May gives 12 marbles to Josh:
Josh = (3/4)j+12;
May = m+(1/4)j-12

Now the two have the same number of marbles:
(2)

There you have 2 equations in j and m; use whatever method you like for solving pairs of equations to solve the problem.

While there are many ways to do that, the path I followed was to solve equation (1) for m and substitute that value in (2).
Answer by KMST(5328)   (Show Source): You can put this solution on YOUR website!
THE ALGEBRA CLASS SOLUTION:
We have two unknown numbers, so we need two variables.
We are given two facts, so we can make two equations.
Choosing variables is an art, but practice makes you a better artist.
My variables:
Josh starts with marbles (n is a positive integer), and is the number of marbles Josh gives May.
May starts with marbles.
Fist Fact: "After Josh gave 1/4 of his marbles to May,
May had 3 times as many marbles as him."
My first equation draft: .
(I can simplify that equation to ).
Second Fact: "May then gave Josh 12 marbles.
In the end, each of them had an equal number of marbles."
My second equation draft: .
(I can simplify that equation to ).
At that point, I solve fornr first,
substituting for in my second equation.
Then, I use the value found to find using the first equation.

THE FIFTH GRADER SOLUTION:
The fifth grader uses trial and error, tabulating results of each try.
Josh starts with a number of marbles that is a multiple of 4.
There are three points in the story:
the start, when Josh has marbles and May has ,
the midpoint, when they have and marbles,
and the end, when they have and marbles.
It could be , or 8, or 12, or 16, and so on.
That would be the first numbered entered on the table.
After he gives 1/4 of his marbles to May, Josh has marbles,
and May has marbles, and those are the next entries.
The fifth grader does not worry about ,
because he realizes try #1 did not work.
He just keeps calculating until he gets to both kids having
the same number of marbles at the end.
Here is the fifth grader's table:

Looking at the line that end in "24 24" ,
the fifth grader realizes that
if May had marbles after receiving marbles from Josh,
she must have started with .
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

            After seeing the solutions from two our respectful tutors, you, probably, have a wish to see something more simple.

            I will try to satisfy this desire by presenting as simple solution as possible. 


From the condition, it is clear that the number of marbles Josh had initially, is multiple of 4.

Let x be  1/4  of Josh's marbles, that he had initially.

So, Josh had initially 4x marbles; at the first exchange, he gave 1/4 of it, i.e. x marbles, to May.

Thus after first exchange, Josh left with 3x marbles, while May had 3 times 3x marbles, i.e. 9x marbles.



After the second exchange, Josh has (3x+12) marbles, while May has (9x-12) marbles.



These amounts are the same, so you have this simple equation

    3x + 12 = 9x - 12.



You can EASILY solve it :

    12 + 12 = 9x - 3x,   or   24 = 6x,   which implies  x= 24/6 = 4.


Thus Josh had initially 4x = 16 marbles.



After first exchange, May had  9x = 9*4 = 36 marbles; but  4 of them came from Josh  (! remember,  x= 4 !),   

so May had initially  36 - 4 = 32 marbles.    ANSWER


Solved.


RELATED QUESTIONS

Hi jane and john had some marbles. After jane gave john some marbles, he had 3 times as... (answered by josgarithmetic)
Juliet gave her 1/5 of her marbles to Ken. After that, Ken gave 2/3 of what he had and an (answered by Edwin McCravy,greenestamps,MathTherapy)
Adam, Ben and Calvin had a total of 540 marbles. Adam gave 1/4 of his marbles to Ben.... (answered by josgarithmetic,ikleyn,MathTherapy,greenestamps)
Jane and Ken had 288 marbles altogether. Jane gave 1/5 of her marbles to Ken. Ken then... (answered by ptaylor)
Hi Kaden and Dan had some marbles. Dan gave away 3/5 as many as Kaden and was left with... (answered by greenestamps)
The ratio of the number of marbles May, Teddy and Sam had was 3:5:2. During a game, May... (answered by ankor@dixie-net.com)
Tony and Peter both had some marbles at first. After Tony gave Peter 4/14 of his marbles, (answered by math_tutor2020,greenestamps,ikleyn)
Hi Amy has 25% as many marbles as Ben. After Ben gave some marbles to Amy,Amy now has... (answered by math_tutor2020,greenestamps)
Julian and Patrick had some marbles. If Julian gave Patrick 20 marbles, both of them... (answered by ikleyn)