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 numbers of cars and y is the number of vans a. graph the equation. interpret the intercepts. the x -intercept shows they can take ___ cars and ___ vans. the y -intercept shows the can take ___ cars and ___ vans. b. find a different possible solution in the context of the problem. they can take ___ cars and ___ vans.

Answer 1

a)

The x-intercept shows that they can take 12 cars and 0 vans.

The y-intercept shows that they can take 0 cars and 8 vans.

b) They can take 3 cars and 6 vans.

They can take 6 cars and 4 vans.

They can take 9 cars and 2 vans.

Step-by-step explanation

The number of players = 48

There are x cars and y vans.

This means the breakdown of how the students will get to the destination is

4x + 6y = 48

a) The graph of the equation is plotted and attached under answers.

The intercepts are then obtained as (0, 8) and (12, 0).

These intercepts represent when either of the modes of transport is absent.

If there are no cars present, (x=0), then the number of vans required = 8

If there are no vans present, (y=0), then the number of cars required = 12

The x-intercept shows that they can take 12 cars and 0 vans.

The y-intercept shows that they can take 0 cars and 8 vans.

b) We are then asked to find a different possible solution in the context of the problem.

This means we need to obtain a feasible point from the graph. Any point on the given line would actually work.

Looking at the graph, we can take a series of solutions (points on the line)

(3, 6), (6, 4) and (9, 2)

So,

They can take 3 cars and 6 vans.

They can take 6 cars and 4 vans.

They can take 9 cars and 2 vans.

Hope this Helps!!!