Question

Lily has

x
x nickels and
y
y dimes. She has no less than 15 coins worth a maximum of $1 combined. Solve this system of inequalities graphically and determine one possible solution.

Answer 1

Lily has at least 15 coins composed of nickels and dimes with a total value no more than $1.00. To find a solution, graph the inequalities x + y ≥ 15 and 0.05x + 0.10y ≤ 1.00, and look for a point within the overlapping region that satisfies both conditions.

Step-by-step explanation:

Lily has x nickels and y dimes. She has at least 15 coins but no more than $1.00 in total value. To solve this system of inequalities graphically, we can set up two inequalities:

1. The total number of coins is at least 15: x + y ≥ 15.
2. The total value is no more than $1.00: 0.05x + 0.10y ≤ 1.00.

We can graph these inequalities on a coordinate plane, with x on the horizontal axis and y on the vertical axis. The area of the graph that satisfies both inequalities represents all possible combinations of nickels (x) and dimes (y) that fit the criteria. One possible solution can be found where the two inequalities intersect within the feasible region on the graph.