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?
:
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?"
{{{(7x-30)/(3x+30)}}} = {{{3/2}}}
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.
{{{(210-30)/(90+30)}}} = {{{3/2}}}