Question

A football team has an away game, and the bus breaks down. The coaches decide to drive the players to the game in cars and vans. Four players can ride in each car. Six players can ride in each van. There are 48 players on the team. The equation 4x + 6y = 48 models this situation, where x is the number of cars and y is the number of vans.a.) Find the x and y-intercept.b.) if there are 2 vans, how many cars will be needed to drive the rest of the players to the game?

Answer 1

Part a

we have the equation

4x+6y=48

where

x is the number of cars and y is the number of vans.

Find the y-intercept (value of y when the value of x is zero)

so

For x=0

4(0)+6y=48

6y=48

y=8

y-intercept is (0,8)

that means -----> the number of vans is 8 when the number of cars is zero

Find the x-intercept (value of x when the value of y is zero)

For y=0

4x+6(0)=48

4x=48

x=12

x-intercept is (12,0)

that means ----> the number of cars is 12 when the number of vans is zero

Part b

For y=2 vans

substitute in the equation

4x+6(2)=48

4x+12=48

4x=48-12

4x=36

x=9

answer part b is 9 cars