Question

Xavier has xx nickels and yy pennies, having no more than 20 coins worth at least $0.40 combined. A minimum of 10 of the coins are nickels and a maximum of 4 of the coins are pennies. Solve this system of inequalities graphically and determine one possible solution.

Answer 1

To solve the system graphically, inequalities based on the number and value of nickels and pennies are plotted. The solution is found where the shaded regions overlap on the coordinate plane. One possible solution is 10 nickels and 4 pennies.

Step-by-step explanation:

We are asked to graphically solve a system of inequalities based on the given constraints and find a possible solution for the number of nickels (x) and pennies (y) Xavier has. Keeping in mind that a nickel is worth 5 cents and a penny is worth 1 cent, we can set up the following inequalities:

• x + y ≤ 20 (total number of coins does not exceed 20)
• 5x + y ≥ 40 (total value is at least 40 cents)
• x ≥ 10 (at least 10 nickels)
• y ≤ 4 (no more than 4 pennies)

To find a solution graphically, we can plot these inequalities on a coordinate plane where the x-axis represents the number of nickels and the y-axis represents the number of pennies.

1. Draw the line x + y = 20. This is the boundary for the total number of coins.
2. Draw the line 5x + y = 40. This is the boundary for the total value in cents.
3. Shade the region where x ≥ 10, which is to the right of the line x = 10.
4. Shade the region where y ≤ 4, which is below the line y = 4.

The solution set is where all the shaded regions overlap. One possible solution from this region might be x = 10 and y = 4. This means Xavier could have 10 nickels and 4 pennies.