Mayerlin has xx dimes and yy nickels. She has no more than 20 coins worth no less than $1.30 combined. Solve this system of inequalities graphically and determine one possible solution.
The given system of inequalities can be represented as follows:
1. xx ≥ 0 (The number of dimes must be greater than or equal to 0)
2. yy ≥ 0 (The number of nickels must be greater than or equal to 0)
3. xx + yy ≤ 20 (The total number of coins must be no more than 20)
4. 0.10xx + 0.05yy ≥ 1.30 (The total value of coins must be no less than $1.30)
To solve this system of inequalities graphically, we will plot these inequalities on a coordinate plane.
First, let's graph the inequality xx + yy ≤ 20:
- Plot the line xx + yy = 20.
- Shade all the points below the line, including the line itself, since it is a less than or equal to inequality.
Next, let's graph the inequality 0.10xx + 0.05yy ≥ 1.30:
- Plot the line 0.10xx + 0.05yy = 1.30.
- Shade all the points above the line, since it is a greater than or equal to inequality.
The graph will consist of two shaded areas: one below the line xx + yy = 20 and another above the line 0.10xx + 0.05yy = 1.30. The feasible solution corresponds to the region where these two shaded areas overlap.
One possible solution in this overlapping region is (xx, yy) = (10, 10). This means Mayerlin has 10 dimes and 10 nickels.
Note: There could be other possible solutions in the overlapping region, but (10, 10) is one of them.