Question

A bus company uses two different sized Buses. The company needs 7 small buses and 5 large buses to
transport 331 people, but needs 4 small buses and 9 large buses to carry 398 people. In these situations all
the busestare full. Determine the number of people each bus can carry.​

Answer 1

Answer:

ets assume small bus can carry - X number of people

      and the large bus can carry - Y number of people

As the buses are people, we can make two quadratic equations like this

  7X + 5Y = 331   and

White it out as an equation.

7 small buses + 5 large buses = 331

7x+5y=331

4 small buses + 9 larges buses = 398

4x+9y=398

x and y being the amount of people the buses can hold respectively. We can then solve by elimating now the variable and solving for the other.

7x+5y=331    

4x+9y=398

4(7x+5y=331)      multiply to ensure the make the oppsite of one variable.

-7(4x+9y=398)

28x+20y=1324   Add them together.

-28x-63y=-2786

-43y=-1462    The X becomes 0 and thus elimated.

y=34

7x+5(34)=331     Plug in the 43 where the y is in one of the equations.

7x+170=331

7x=161

x= 23

So then you find out that small buses carry 23 people and larger buses carry 34.