Question

Brianna has x nickels and y pennies. She has no less than 20 coins worth no more

Answer 1

Answer:

$y \ge 20 - x$

$y \le 80 -5x$

$(x,y) = (15,5)$

Step-by-step explanation:

Given

$Nickels = x$

$Pennies = y$

$Amount = \ 0.80$ maximum

$Coins = 20$ minimum

Required

Solve graphically

First, we need to determine the inequalities of the system.

For number of coins, we have:

$x\ +\ y\ge 20$ because the number of coins is not less than 20

For the worth of coins, we have:

$0.05x\ +\ 0.01y\ \le0.80$ because the worth of coins is not more than 0.80

So, we have the following equations:

$x\ +\ y\ge 20$

$0.05x\ +\ 0.01y\ \le0.80$

Make y the subject in both cases:

$y \ge 20 - x$

$0.01y \le 0.80 - 0.05x$

Divide through by 0.01

$\frac{0.01y}{0.01} \le \frac{0.80}{0.01} -\frac{ 0.05x}{0.01}$

$y \le \frac{0.80}{0.01} -\frac{ 0.05x}{0.01}$

$y \le 80 -5x$

The resulting inequalities are:

$y \ge 20 - x$

$y \le 80 -5x$

The two inequalities are plotted on the graph as shown in the attachment.

$y \ge 20 - x$ --- Blue

$y \ge 80 -5x$ --- Green

Point A on the attachment are possible solutions

At A:

$(x,y) = (15,5)$