By solving the system of inequalities graphically, one possible solution is 6 dimes and 20 nickels. Therefore, the solution as an ordered pair is (6, 20).
In order to determine the number of dimes and nickels, we would assign a variables to the unknown numbers and then translate the word problem into algebraic equation as follows:
- Let the variable y represent number of nickels.
- Let the variable x represent the number of dimes.
Note: 1 nickel is equal to 0.05 dollar and 1 dime is equal to 0.1 dollar.
Since Jackson has at least 22 coins worth at most $1.70 combined, an equation that models this situation is given by;
0.10x + 0.05y ≤ 1.70 ....equation 1.
Additionally, no less than 4 of the coins are dimes and a maximum of 22 of the coins are nickels;
x ≥ 4 ....equation 2.
x + y ≤ 22 ....equation 3.
By solving the system of inequalities graphically using an online graphing tool, one possible solution is 6 dimes and 20 nickels.
Complete Question:
Jackson has x dimes and y nickels, having at least 22 coins worth at most $1.70 combined. No less than 4 of the coins are dimes and a maximum of 22 of the coins are nickels. Solve this system of inequalities graphically and determine one possible solution.