Question

Arianna has x nickels and y pennies, having no more than 20 coins worth a minimum of $0.40 combined. At least 10 of the coins are nickels. Solve this system of inequalities graphically and determine one possible solution.

Answer 1

Explanation:

x = nickels

y = pennies

x + y <= 20

0.05x + 0.01y >= 0.40

x >= 10

Now, we have the system of equations. If we know that there is at least 10 nickels, then we can plug in a number which will fit. Now, we need to draw a graph for this so let's use desmos. The shaded area shows the solutions which you can use. The shaded area is the area with a mixture of red and green and is in the intersection. Now, although all of the answers in the shaded area would work, you need to have a positive number because you can not have negative nickels or pennies. Due to this, choose anything in the shaded area of the first quadrant.