Answer
There were 2 buses and 4 vans.
Work Step by Step
Set up two equations: x+y=6 and 51x+10y=142. X represents the buses and the Y represents the cars. Isolate the y in the first equation in order to be able to substitute it into the first equation:
x+y=6 -subtract x from both sides-
y=6-x
Substitute the equation into the second equation:
51x+10y=142 -substitute-
51x+10(6-x)=142 -distribute-
51x+60-10x=142 -simplify like terms-
41x+60=142 -subtract 60 from both sides-
41x=82 -divide both sides by 41-
x=2
Substitute x=2 into one of the equations:
2+y=6 -subtract 2 from both sides-
y=4
Check the solution:
51x+10y=142
51(2)+10(4)=142
102+40=142
142=142
There were 2 buses and 4 vans.
