This year, 713 students went to a summer camp in 25 buses, some of which had 33 seats, and some 26 seats. If the students filled all the bus seats, how many buses had 33 seats and how many 26 seats?
Answers
Answer: Bus with 33 seats = 9 , with 26 seats = 16
Explanation: Let no. of bus with seats 33 be x , and no. of Bus with 26 be y.
According to question:-
x+y=25 ( total bus is 25)-> (i)
33x+26y=713( total students is 713) -> (ii)
On multiplying eq (i) by 26 we get 26x + 26y = 650 ->(iii)
On subtracting eq(ii) & eq (iii)
7x=63
x=9
On Putting value of x in eq(i)
9+y=25
y=16
Therefore no. of Bus with 33 seats = x = 9, no. of Bus with 26 seats = y = 16 ANS
Given: Total number of students = 713
Total number of buses = 25
To find: Number of buses with 33 and 26 seats
Let: Number of buses with 33 seats = X
Number of buses with 26 seats = Y
Solution: According to the given question,
Students have filled all the bus seats i.e., no seat is left empty
The required equation will be
33X + 26Y = 713 ...(1)
also, total number of buses = 25
i.e., X + Y = 25 ...(2)
Multiplying equation (2) with 33
⇒ 33X + 33 Y = 33 x 25
⇒ 33X + 33Y = 825
⇒ 33X = 825 - 33Y
Putting value of 33X in equation (1)
⇒ (825 - 33Y) + 26 Y = 713
⇒ 33Y - 26Y = 825 - 713
⇒ 7Y = 112
Y = 112/7
Y = 16
Putting value of Y in equation (2)
X + 16 = 25
X = 25 - 16 = 9
Hence, number of buses with 33 seats (X) = 9
and number of buses with 26 seats (Y) = 16