Question

The Marching Band is traveling from Minnesota to Florida to perform in a national competition. A train ticket from Minnesota to Florida costs $150 and takes 15 hours of travel time per student. To rent a bus to make the trip, it costs $120 per student and takes 20 hours of travel time per student. The band has $4,800 to spend on the trip and can only spend 720 hours of total travel time. Use the information below.Let x = Students traveling by trainLet y = Students traveling by busTherefore,$150x + $120y < $4,800 and15x + 20y < 720.The graph of these functions is to the right.It is impossible for a negative number of students to go on the trip, so x and y both have to be greater than zero. Therefore, the functions are confined to the first quadrant.Number of students function:N = x + yWhat is the maximum number of students who can attend the trip? A. A maximum of 36 students can attend the trip. B. A maximum of 32 students can attend the trip. C. A maximum of 38 students can attend the trip. D. A maximum of 40 students can attend the trip.

Answer 1

A maximum of 38 students can attend the trip. (Option C).

Step-by-step explanation

Given:

Number of students function: N = x + y

$150x + $120y < $4,800 ................equ 1

15x + 20y < 720.................................equ 2

where

x = Students traveling by train

y = Students traveling by bus

Multiply equation 2 by -10

`equ\text{ 2 }*-10\Rightarrow-150x\text{ - 200y < -7200..........................equ 3}`

Add equation 1 and 3

150x + 120y < 4,800

-150x - 200y <-7200

-----------------------------

0x - 80y < -2400

y > 2400/80

y > 30

Substitute the value of y into equation 1 to solve for x

150x + 120y < 4,800

150x + 120(30) < 4800

150x < 4800 - 3600

x < 1200/150

x < 8

Number