Question

A class of 165 students went on a field trip. They

took 9 vehicles - some were cars and some were
Suses. Find the number of cars and the number
of buses they took if each car holds 5 students
and each bus holds 45 students. Show your work.

Answer 1

the number of buses is 3

the number of cars is 6

Explanation:

total number of the students=165

total number of the vehicles=9

let x represent the number of cars

let y represent the number of buses

x+y=9...........equation 1

(the number of the cars plus the number of the buses= to the number of vehicles )

5x + 45y=165.......equation 2

(the number of student the car can hold plus the number of student the bus can hold= to the total number of the student in a class)

x+y=9.......eqn 1

5x +45y=165....eqn 2

make x the subject of the formula in eqn 1

x+y=9

x= 9-y

substitute for x= 9-y in eqn 2

5(9-y)+45y=165

45-5y+45y=165

-5y+45y=165-45

40y=120

divide both sides by 40

40y÷40=120÷40

y=3

since y represent number of buses,the numbet of bus is 3

Also,substitute for y=3 in eqn 1

eqn 1 is x+y=9

x+3=9

x=9-3

x=6

therefore,the number of cars is 6.