SOLUTION: Fred and Tom mowed lawns for a day. Fred earned x/y times as much money as did Tom. Determine what fraction of total money earned was Tom's. Not sure how to solve.

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Question 1197736: Fred and Tom mowed lawns for a day. Fred earned x/y times as much money as did Tom.
Determine what fraction of total money earned was Tom's.
Not sure how to solve.
Found 3 solutions by ikleyn, math_tutor2020, MathTherapy:
Answer by ikleyn(52832) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let M be the money earned by Tom.


Then Fred earned %28x%2Fy%29%2AM money.


Total they earned is this sum  T = M+%2B+%28x%2Fy%29%2AM = M%2A%281%2Bx%2Fy%29.    (1)


We want to express M via T.


From (1),  M = T%2F%281%2Bx%2Fy%29.    (2)


It is the expression you want to get.

Solved.

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Keep in mind that the final formula in the post by @josgarithmetic is incorrect

                    highlight%28cross%28T%2F%28T%28x%2Fy%29%2B1%29%29%29


How do I know it ?   - - -   Because his formula mixes in the denominator values with dimension of money
                                          with dimensionless value of  1.


So,  ignore his post for the safety of your mind.


////////////////


comment from student :  Why was 1 added to x/y ?


My response :  My formula  (2)  follows directly from formula  (1).

                       Simple algebra.   If you don't know it (asking such question),  it means that you are in wrong class  (if any).



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

This is a supplement to @ikleyn's post.

The student asks "Why was 1 added to x/y?"

A better response would be to say "Because we factored out the M from M+%2B+%28x%2Fy%29%2AM to end up with M%2A%281%2Bx%2Fy%29"

The distributive rule is being applied
a*(b+c) = a*b+a*c
Factoring is effectively going in reverse of distributing.

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
Fred and Tom mowed lawns for a day. Fred earned x/y times as much money as did Tom.
Determine what fraction of total money earned was Tom's.
Not sure how to solve.
Let amount Tom earned, be T
Since Fred earned x%2Fy times as much money as did Tom, Fred earned %28x%2Fy%29T.  
Together, they made: matrix%281%2C3%2C+T+%2B+%28x%2Fy%29T%2C+or%2C+T%281+%2B+x%2Fy%29%29

Fraction of total money, earned by Tom: