Hong Kong
Stage 4 - Stage 5

# Problems with Systems of Inequalities in 2 Variables

## Interactive practice questions

An airline is checking passengers into two flights, A and B, simultaneously. Due to passenger numbers, there must be at least $10$10 staff at check-in for flight A and at least $7$7 staff at check-in for flight B. Since there must be staff on hand for other services, the airline can only allocate at most $23$23 staff for check-in of both flights.

a

Let $x$x and $y$y represent the number of staff attending check-in of flights A and B respectively.

Fill in the gaps to complete the system of inequalities.

$x$x $\ge$ $\editable{}$

$y$y $\ge$ $\editable{}$

$x+y$x+y $\le$ $\editable{}$

b

Graph the system of inequalities.

c

If $14$14 staff are allocated to checking in passengers of flight A, what is the maximum number of staff that can be allocated to checking in passengers of flight B?

Easy
4min

Roald has $24$24 inches of leftover wood that he is trying to make a rectangular photo frame out of.

Easy
3min

Applicants for a particular university are asked to sit a numeracy test and verbal reasoning test. Successful applicants must obtain a minimum score of $17$17 on a numeracy test and a minimum combined score of $37$37 for both tests.

Medium
3min

There are $x$x surfers competing for wildcard entry into a pro-surfing competition, of which Joanne is one. She needs her total score from all judges, $y$y, to be at least $35$35 in order to be chosen as a wildcard entry. The total score possible from all judges is at most $50$50.

Medium
4min