Question

Mav has xx nickels and yy dimes. She has no more than 28 coins worth a minimum of $2 combined. Solve this system of inequalities graphically and determine one possible solution.

inequality #1-
inequality #2-
mav could have __ nickles and __ dimes

Answer 1

Inequality #1: x + y ≤ 28

Inequality #2: 0.05x + 0.1y ≥ 2

Mav could have 5 nickles and 20 dimes.

Explanation:

It's given that Mav has less than or equal to 28 coins, so we can write the following inequality:

x + y ≤ 28

We know that a nickel is work 0.05 and a dime is worth 0.1. Using the given information, the following inequality is true since the coins must be greater than or equal to $2 combined:

0.05x + 0.1y ≥ 2

Now, we will graph them. Both graphed lines will use solid lines since both include equal to. We will shade below #1 and above #2. I used Desmos Graphing Calculator, you can find it online for free. Once we type in our equations, we get the needed graph.

The overlapping portion contains our possible solutions. There are many, but one possible solution is (5, 20), with 5 nickels and 20 dimes.