SOLUTION: When Butch and Kent left for their trip, the ratio of Butch's money to Kent's money was 7:3. After a short while Butch gave Kent $30, making the new ratio of their cash 3:2. When t

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Question 719919: When Butch and Kent left for their trip, the ratio of Butch's money to Kent's money was 7:3. After a short while Butch gave Kent $30, making the new ratio of their cash 3:2. When they started the trip how much more money did Butch have than Kent?
How to solve this problem the correct way? I got the answer by process of elimination (just plugging in numbers till I found the correct answer) but I would like to know how to solve the problem the correct way.
For the first ratio 7:3, I found that Butch started with $210 and Kent with $90 (ratio 7:3)(7x30=210, 3x30=90). So Butch had $120 more than Kent when they started.
For the second ratio 3:2, if Butch gave Kent $30 he would have $180 (210-30=180) and Kent would have $120 (90+30=120) ending up with the correct 3:2 ratio. (3x60=180, 2x60=120).
But how can this be solved without just plugging in numbers until the correct answer is found? Thank you.
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
When Butch and Kent left for their trip, the ratio of Butch's money to Kent's money was 7:3.
After a short while Butch gave Kent $30, making the new ratio of their cash 3:2. When they started the trip how much more money did Butch have than Kent?
:
Let x = the multiplier
then
7x = B's original amt
and
3x = K's amt
:
After a short while Butch gave Kent $30, making the new ratio of their cash 3:2. When they started the trip how much more money did Butch have than Kent?"
=
cross multiply
2(7x-30) = 3(3x+30)
14x - 60 = 9x + 90
14x - 9x = 90 + 60
5x = 150
x = 30 is the multiplier
then
7(30) = $210 was B's amt
3(30) = $90 was K's amt
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differ: $120 amt B had more than K
:
:
You can confirm this, find the ratio of how much they had after the $30 exchange.
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