EDGE Math 8

Example 3

Mother's weekly budget for fish and chicken is at most ₱1200. Note that 1 kg of fish costs ₱60, while 1 kg of chicken costs ₱120.

a.	Write a system of inequalities for the given situation. Then graph the solution set of the system.
b.	Determine if the ordered pair $(10, 7)$ is a solution to the system.

Solution

a.	Let x = number of kilograms of fish and y = number of kilograms of chicken.

The weekly budget for fish and chicken is at most ₱1200. This statement translates into

60 x + 120 y \leq 1200.

Moreover,

x \geq 0

and

y \geq 0.

You now have the following system of inequalities:

{\begin{array}{l} 60 x + 120 y \leq 1200 \\ x \geq 0 \\ y \geq 0 \end{array}

The graph representing the solution set of the inequality

60 x + 120 y \leq 1200

is the region on or below the boundary line

60 x + 120 y = 1200.

The inequalities

x \geq 0

and

y \geq 0

restrict the solution set of the system to the first quadrant region together with the nonnegative sides of the x- and y-axes.

Refer to the following figure for the graph of the solution set of the system:

b.	Substituting $x = 10$ and $y = 7$ in the inequality $60 x + 120 y \leq 1200,$ you will get

\begin{array}{l} 60 (10) + 120 (7) \leq 1200 \\ 1440 \leq 1200, \end{array}

which is false.

Hence,

(10, 7)

is not a solution of the system. As shown in the graph above, the point

(10, 7)

lies outside the shaded region.