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! .
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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