b Let d represented by the x-axis and c represented by the y-axis. Begin by determining the boundary line.
C
c The possible solutions for the number of DVDs and CDs are in the shaded region. Choose three points with whole number coordinates. There can be more than three point.
A
a 20d+15c≤ 400
B
bGraph:
C
cPossible Solutions:
4 DVDs, 4 CDs
8 DVDs, 8 CDs
12 DVDs, 4 CDs
Practice makes perfect
a To write an inequality that represents the situation, we will organize the given information on a table. Notice that the total cost cannot exceed $400.
Verbal Expression
Algebraic Expression
Cost of d DVDs ($)
20 d
Cost of c CDs ($)
15 c
The total cost must be less than or equal to $400
20 d+15 c≤400
b We can graph the inequality by finding its boundary line. It can be found by replacing the inequality symbol with the equals sign.
&Inequality &&Boundary Line
&20d+15c ≤ 400 &&20d+15c = 400
Let d represented by the x-axis and c represented by the y-axis. We will draw the line by finding its intercepts. Let's first find its x-intercept (d-intercept) by substituting 0 for c.
Thus, the y-intercept is about 26.7. We will plot these points and connect them with a line segment. The line will be solid because the inequality is non-strict. Since the number of DVDs and CDs cannot be negative, the line will also be bound by the axes.
In the final step, we will test an arbitrary point to decide which region we should shade. We will test the point (0,0) to make the math bit easier.
