In a bus, there were 3/4 as many adults as children. after 14 adults boarded the bus, the number of children was 2/5 of the number of adults. how many adults were there in the bus at first?

There were 6 adults on the bus to start with.

We can set up a system of equations to solve this:
A = 3/4C
2/5(A+14) = C

We will substitute the value for the first equation into the second equation to solve:

2/5(3/4C+14) = C

Using the distributive property, we have:
2/5(3/4C) + 2/5(14) = C
6/20C + 28/5 = C

It's usually easier to not deal with fractions.  Since th denominators of both fractions will go into 20, we will multiply everything in the equation by 20:

20(6/20C) + 20(28/5) = 20(C)
6C + 560/5 = 20C
6C + 112 = 20C

Subtract 6C from both sides:
6C + 112 - 6C = 20C - 6C
112 = 14C

Divide both sides by 14:
112/14 = 14C/14
8 = C

Plugging this back into the first equation, we have:
A = 3/4(8) = 24/4 = 6.