SOLUTION: For a trip, one high school rented and filled 6 vans and 8 buses with 202 students. Another high school instead fit its 68 students into 4 vans and 2 buses. With each bus and van s

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Question 1135543: For a trip, one high school rented and filled 6 vans and 8 buses with 202 students. Another high school instead fit its 68 students into 4 vans and 2 buses. With each bus and van seating the same number of students, how many students can a bus carry? How many students can a van carry?
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
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Let x = capacity of a van and y = capacity of a bus.


From the condition, you have these two equations

    6x + 8y = 202   (1)
    4x + 2y =  68   (2)


In this case, I will apply the Elimination method. I multiply eq(2) by 4 (both sides), keeping equation (1) as is.


    6x + 8y = 202    (1')
   16x + 8y = 4*68   (2')


Now subtract eq(1') from eq(2').  The terms " 8y " will cancel each other, and you will get

    16x - 6x = 4*68 - 202,    or

    10x = 70   ================>  x = 70/10 = 7.


Now substitute this found value of x into eq(2) to find y. You will get


    4*7 + 2y = 68,

    2y = 68 - 28 = 40  ============>  y = 40/2 = 20.


ANSWER.  Van's capacity is 7 students;  bus' capacity is 20 students.

Solved.


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