Math

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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...

  • Math -

    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(x-3) = 46
    2x + 3x - 9 = 46
    5x = 55
    x = 11

    if x = 11, then y = x-3 = 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

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