SOLUTION: Hi Stephen and Siew mei had $540 altogether. Stephen gave 1/7 of his money siew mei. In return siew mei gave 1/4 of the total amount she had to Stephen . Then they both had the sa

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Hi Stephen and Siew mei had $540 altogether. Stephen gave 1/7 of his money siew mei. In return siew mei gave 1/4 of the total amount she had to Stephen . Then they both had the sa      Log On

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Question 1189297: Hi
Stephen and Siew mei had $540 altogether. Stephen gave 1/7 of his money siew mei. In return siew mei gave 1/4 of the total amount she had to Stephen . Then they both had the same amount of money. How much did Stephen had at first.
Thanks
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52777) About Me  (Show Source):
You can put this solution on YOUR website!
.
Stephen and Siew Mei had $540 altogether.
Stephen gave 1/7 of his money Siew Mei.
In return Siew Mei gave 1/4 of the total amount she had to Stephen .
Then they both had the same amount of money. How much did Stephen had at first ?
~~~~~~~~~~~~~~~~~~ 


Let x be the amount which Stephan had at first.

Then Siew Mei had (540-x) dollars at first.


When Stephen gave 1/7 of his money to Siew Mei, Stephen left with %286%2F7%29x dollars;

Siew Mei had %28540-x%29+%2B+%281%2F7%29x.


When Siew Mei gave 1/4 of the total amount she had to Stephen, she left with %283%2F4%29%2A%28%28540-x%29+%2B+%281%2F7%29x%29.

Stephen had finally %286%2F7%29x + %281%2F4%29%2A%28%28540-x%29%2B%281%2F7%29x%29 dollars.


The final amounts are the same, so we write this equation

    %283%2F4%29%2A%28%28540-x%29%2B%281%2F7%29x%29 = %286%2F7%29x + %281%2F4%29%2A%28%28540-x%29%2B%281%2F7%29x%29.


Simplify this equation and find x. First multiply both sides by 4*7 = 28
    
    3*7*((540-x) + (1/7)*x) = 6*4x + 7*((540-x)+(1/7)x)

    21*(540-x) + 3x = 24x + 7*(540-x) + x

    14*(540-x) = 22x

    14*540 = 22x + 14x

    14*540 = 36x

    x = %2814%2A540%29%2F36 = 210.


ANSWER.  Stephen had initially 210 dollars;  Siew Mei had initially 540-210 = 330 dollars.


CHECK.  After first giving, Stephen had 210-30 = 180 dollars; Siew Mei had 330+30 = 360 dollars.

        After second giving, Stephen had 180 + 90 = 270 dollars; Siew Mei had 360-90 = 270 dollars.   ! Equal amounts, correct !

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


There are many ways to set up this problem for solving. The solution from the other tutor is fine, and is a very typical solution.

I personally would choose a different starting point by looking ahead at the transactions to perhaps make the algebra required for solving the problem a bit easier.

Specifically, since in the first transaction Stephen gives 1/7 of his money to Siew Mei, I would start with

let 7x = amount Stephen starts with
then 540-7x = amount Siew Mei starts with

In the first transaction, Stephen gives 1/7 of his money, x, to Siew Mei. The amounts the two have are now 6x for Stephen and 540-6x for Siew Mei.

Next Siew Mei gives 1/4 of her money, 135-1.5x, to Stephen. The amounts they have are now 135+4.5x for Stephen and 405-4.5x for Siew Mei.

The amounts they have now are the same, so they are both half of $540, which is $270. So we can either solve the equation that says those two expressions are equal; or we can solve an equation that says one of those two expressions is equal to 540/2=270.

135%2B4.5x=270
4.5x=135
9x=270
x=30

ANSWER: The amount Stephen started with was 7x=$210