
78 students went on a field trip. They went by van or car. The total number of cars and vans were 10. Each car held 5 students and each van held 12 students. How many cars and how many vans went on the field trip?
Let the number of cars be "x" and the number of vans be "y".
According to question,
x + y = 10 5x + 12y = 78 -->(ii)
=> 5(x + y) = 10 × 5
=> 5x + 5y = 50 -->(i)
By Elimination method,
Equation (i) - (ii) we get,
(5x + 5y) - (5x + 12y) = 50 - 78
=> 5x + 5y - 5x - 12y = - 28
=> - 7y = - 28
=> 7y = 28
=> y = 28/7
=> y = 4
Putting the value of "y" in Equation (i)
5x + 5y = 50
=> 5x + 5 × 4 = 50
=> 5x + 20 = 50
=> 5x = 50 - 20
=> 5x = 30
=> x = 30/5
=> x = 6
The total number of cars went = 6
The total number of vans went = 4
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168 students went on a field trip. They took a total of 10 vans and buses. Each bus held 42 students, and each van held 6 students. How many vans went on the field trip?
Solution:
Let the number of buses be "x" and the number of vans be "y".
According to question,
x + y = 10 42x + 6y = 168 -->(ii)
=> 42(x + y) = 10 × 42
=> 42x + 42y = 420 -->(i)
By Elimination method,
Equation (i) - (ii)
(42x + 42y) - (42x + 6y) = 420 - 168
=> 42x + 42y - 42x - 6y = 252
=> 36y = 252
=> y = 252/36
=> y = 7
Putting the value of "y" in Equation (ii)
42x + 6y = 168
=> 42x + 6 × 7 = 168
=> 42x + 42 = 168
=> 42x = 168 - 42
=>42x = 126
=> x = 126/42
=> x = 3
Total number of buses went = 3
Total number of vans went = 7