SOLUTION: Hi at first the ratio of bob and teds money was 5 to 2 . After each of them spent an equal amount the ratio of bob to teds became 6 to 1 . In the end they had a total 126 dollars.

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Question 1148436: Hi
at first the ratio of bob and teds money was 5 to 2 . After each of them spent an equal amount the ratio of bob to teds became 6 to 1 . In the end they had a total 126 dollars. How much did they spend together.
Thanks
Found 3 solutions by josgarithmetic, ikleyn, greenestamps:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
x, the equal part that each spent
b, Bob's money at the start
t, ted's money at start
.
.


not a finished solution
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

From the condition, Bob and Ted had initially  5x and 2x dollars, respectively.


Then each of them spent equal amount of "y" dollars.


After that, they  possessed  5x-y  and  2x-y dollars respectively, and  


     =  = 6,

so

    5x-y = 6*(2x-y),

    5x - y = 12x - 6y

     5y = 7x.            (1)


Also, we are given that

    (5x-y) + (2x-y) = 126  dollars,   or


     7x - 2y = 126.      (2)


In (2), replace  7x  by  5y, based on (1).  You will get


    5y - 2y = 126,

    3y      = 126

     y      = 126/3 = 42.


Then from (1),  x =  =  = 5*6 = 30.


ANSWER.  Initially, they had  5x + 2x = 7x = 7*30 = 210 dollars.

Solved.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


You have received responses (1) outlining a solution using three variables and (2) showing a complete solution using two variables.

Here is a solution using only one variable (although it is use more than once, for different reasons).

(1) They ended up with 126 dollars, in the ratio 6:1. So





The amounts they ended up with were x = $18 and 6x = $108.

(2) The difference between the amounts they ended up with was $108-$18 = $90; and they spent the same amount. So the difference between the amounts they started with was $90.

The amounts they started with were in the ratio 5:2; call those amount 5x and 2x. The difference is 3x, which we know is $90. So




So the amounts the two started with were 5x = $150 and 2x = $60.

So together they started with $150+$60 = $210; and they finished with $126. So the amount they spent was $210-$126 = $84.
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