Math
posted by Brandi on .
I need help on how to work the problem below. The teacher said the answer is 11, but I don't understand how you get there.
"The Big Screamer Coaster carries 92 people altogether. Some if its cars carry 4 passengers,and the rest carry 6 passengers. There are 3 less 6 passenger cars than 4 passenger cars. How many 4 passenger cars are there?"
Thanks...

number of 4 passenger cars  x
number of 6 passenger cars  y
assuming the coaster is filled to capacity ...
4x + 6y = 92 or 2x + 3y = 46
but y = x  3
sub into first equation ....
2x + 3y = 46
2x + 3(x3) = 46
2x + 3x  9 = 46
5x = 55
x = 11
if x = 11, then y = x3 = 8
there are 11 four passenger cars and 8 six passenger cars
check:
4(11) + 6(8) = 92
and 8 is 3 less than 11