Answer:
[tex]y \ge 20 - x[/tex]
[tex]y \le 80 -5x[/tex]
[tex](x,y) = (15,5)[/tex]
Step-by-step explanation:
Given
[tex]Nickels = x[/tex]
[tex]Pennies = y[/tex]
[tex]Amount = \$0.80[/tex] maximum
[tex]Coins = 20[/tex] minimum
Required
Solve graphically
First, we need to determine the inequalities of the system.
For number of coins, we have:
[tex]x\ +\ y\ge 20[/tex] because the number of coins is not less than 20
For the worth of coins, we have:
[tex]0.05x\ +\ 0.01y\ \le0.80[/tex] because the worth of coins is not more than 0.80
So, we have the following equations:
[tex]x\ +\ y\ge 20[/tex]
[tex]0.05x\ +\ 0.01y\ \le0.80[/tex]
Make y the subject in both cases:
[tex]y \ge 20 - x[/tex]
[tex]0.01y \le 0.80 - 0.05x[/tex]
Divide through by 0.01
[tex]\frac{0.01y}{0.01} \le \frac{0.80}{0.01} -\frac{ 0.05x}{0.01}[/tex]
[tex]y \le \frac{0.80}{0.01} -\frac{ 0.05x}{0.01}[/tex]
[tex]y \le 80 -5x[/tex]
The resulting inequalities are:
[tex]y \ge 20 - x[/tex]
[tex]y \le 80 -5x[/tex]
The two inequalities are plotted on the graph as shown in the attachment.
[tex]y \ge 20 - x[/tex] --- Blue
[tex]y \ge 80 -5x[/tex] --- Green
Point A on the attachment are possible solutions
At A:
[tex](x,y) = (15,5)[/tex]
