Question

All Pre-Calculus students at a school were invited to go on a field trip that was offered over three different weeks. A total of 299 people attended. They traveled on the field trip by buses, vans and cars.

• In week 1, a total of 97 students went on the trip using 3 buses, 2 vans, and 1 car to get there.
• In week 2, 109 students traveled on the trip using 4 buses and only 1 van.
• In week 3, 93 students traveled using 2 buses, 3 vans, and 4 cars.

Let "b" represent the number of students that traveled by bus

Let "v" represent the number of students that traveled by van

Let "c" represent the number of students that traveled by car

Solve the matrix equation for the given scenario above using technology. Based on your solution, how many students traveled by bus?

Answer 1

equations describing given situation are

3b+2v+1c=97
4b+1v+0c=109
2b+3v+4c=93

matrix representation is

|A|=3((1*4)-(3*0))-2((4*4)-(2*0))+1((4*3)-(2*1))
=>|A|=3(4)-2(16)+1(10)
=>|A|=12-32+10
=>|A|=-10

|A₁|=97((1*4)-(3*0))-2((109*4)-(93*0))+1((109*3)-(93*1))
=>|A₁|=97(4-0)-2(436-0)+1(327-93)
=>|A₁|=388-872+234
=>|A₁|=-250

using crammers rule

Therefore 25  students traveled by bus