Application of inequalities in two variables

Example:

One class in a school had “g’ girls and “b” boys. The class cannot take more than 40 pupils. It is found that more than half of the pupils are boys, but there are always at least 14 girls.

(a) Write down three inequalities in “g” and “b”
(b) Draw graphs to show these inequalities
(c) Shade properly the area that correctly describes the situation above

EXERCISE

A business man employs x men and y women. He can afford to employ not more than 16 people. Because there is some heavy work to be done he needs more than 4 men. But some precise work can be done better by women so he needs at least 6 women

(a) Write down three inequalities involving x and y
(b) Draw a graph to show these three inequalities
(c) Use your graph to find out the maximum number of men he can employ and the maximum number of women he can employ.
(d) What is the smallest number of people he can employ

Assignment

(1) The longer side of a rectangle are each “a” metres and the shorter sides are each “b” metres. The sides of the rectangle are at least 10cm and the shorter sides are less than 10cm. The perimeter is less than 50cm.
(a) Write down three inequalities involving a and b
(b) Draw the graph to show these inequalities
(c) Shade correctly the area that best describes the above situation