Context Inequality Systems

Question

Austin has x nickels and y dimes, having a maximum of 15 coins worth a minimum of $1 combined. No more than 4 of the coins are nickels and no less than 11 of the coins are dimes. Solve this system of inequalities graphically and determine one possible solution.

Answer 1

As it says, graph these constraints (I prefer n,d to x,y): n + d ≤ 15, 5n + 10d ≥ 100, n ≤ 4, d ≥ 11. The second constraint simplifies to n + 2d ≥ 20, with the boundary line plotted as n = 20 - 2d or d = 10 - 1/2 n. When everything is plotted, you will find a small region of values satisfying all constraints. (n,d) = (2,12) is the point in the middle of this region.