1. In this question you must show all stages of your working.

A college offers only three courses: Construction, Design and Hospitality. Each student enrols on just one of these courses. In 2019, there was a total of 1110 students at this college.
There were 370 more students enrolled on Construction than Hospitality.
In 2020 the number of students enrolled on

• Construction increased by \(1.25 \%\)
• Design increased by \(2.5 \%\)
• Hospitality decreased by \(2 \%\)

In 2020, the total number of students at the college increased by \(0.27 \%\) to 2 significant figures.

1. 1. Define, for each course, a variable for the number of students enrolled on that course in 2019.
   2. Using your variables from part (a)(i), write down three equations that model this situation.
2. By forming and solving a matrix equation, determine how many students were enrolled on each of the three courses in 2019.