A graph of the system of inequalities is shown in the image and one possible solution is the ordered pair (2, 10).
Nichelle can have 2 dimes and 10 nickels.
In order to solve these system of inequalities graphically, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
- Let x represent number of dimes.
- Let y represent number of nickels.
Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.
Since Nichelle has at least 11 coins worth a maximum (at most) of $0.80 combined, a linear inequality to represent this is given by;
x + y ≥ 11
y ≥ 11 - x
For a maximum of $0.80 combined, we have:
0.1x + 0.05y ≤ 0.80
y ≤ -2x + 16
Based on the graph (see attachment), a possible solution is given by the ordered pair (2, 10). Therefore, Nichelle can have 2 dimes and 10 nickels worth of coins.