SOLUTION: 2/5's of A's money is equal to 2/3's of B's money. Total of their money is $4800. Determine A and B's money. 2/5 of A's = 2/3's of B's. A + B = 4800. Not sure how to pro

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Question 1163258: 2/5's of A's money is equal to 2/3's of B's money. Total of their money is $4800. Determine A and B's money.
2/5 of A's = 2/3's of B's.
A + B = 4800.
Not sure how to proceed.

Found 3 solutions by Boreal, greenestamps, ikleyn:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
that's a good start
multiply the first by 15 to clear fractions
6A=10B
3A=5B. then A=(5/3) B, to bring a fraction back which can be more easily substituted.
A+B=4800
(5/3)B+B=4800. (5/3)+B is (5/3)B+(3/3)B, common denominator. They add to (8/3)B
(8/3)B=4800
B=4800*3/8=$1800
A=$3000
2/5 s of A is $1200
2/3s of B is $1200
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!




So the ratio of A's money to B's money is 3:5.

So divide the total $4800 into two parts in the ratio 3:5.

A has more money than B, so

3x = B's money
5x = A's money





A's money is 5x = $3000
B's money is 3x = $1800

CHECK:
(2/5)($3000) = 2($600) = $1200
(2/3)($1800) = 2($600) = $1200
Answer by ikleyn(52798)   (Show Source): You can put this solution on YOUR website!
.

From the condition, you have

     = .    (1)


Multiply both sides by 3*5 = 15.   You will get

    6A = 10B,   or

    3A = 5B.         (2)


You have also second equation
    
    A + B = 4800.    (3)


Multiply its both sides by 3.  You will get

    3A + 3B = 3*4800 = 14400.


In the left side, replace 3A by 5B, based on equation (2).  You will get

    5B + 3B = 14400,  or

    8B      = 14400,

     B      = 14400/8 = 1800.


So, the amount B is just found: it is 1800 dollars.


The last step is to find A. For it, subtract 1800 from 4800

    A = 4800 - 1800 = 3000 dollars.


ANSWER.  A has $3000;  B has $1800.


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comment from student: Why did you multiply equation (3) by 3 ?
-------------


My response : Good question, thanks for asking. 

    I multiply equation (3) by 3  in order for to have this term " 3A ", which I later replace by  " 5B ".


    My secret goal is to get an equation for one unknown " B " only, and for it I make all these transformations.


Is everything clear to you now ?

If you still have questions, do not hesitate to post them to me . . .


Have a nice day (!)


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comment from student:   How did you get 3A = 5B from 6A = 10B ?
-------------


My response :   I divided both sides of the equation  6A = 10B  by  2.



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