Question

Madelyn has x nickels and y dimes, having a maximum of 15 coins worth no

less than $1 combined. At least 2 of the coins are nickels and at least 9 of the
coins are dimes. Solve this system of inequalities graphically and determine
one possible solution.

Answer 1

9514 1404 393

Answer:

2 nickels, 9 dimes

Explanation:

When there are a number of overlapping shaded areas on the graph, I find it convenient to use the reverse of the inequalities. That makes the unshaded area the solution space. Here, the vertices of the triangular solution space are ...

(2, 9), (2, 13), (6, 9)

Any of the grid points within (or on) this triangle is a possible solution. One of them is (2, 9) corresponding to 2 nickels and 9 dimes.

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Three solutions are shown:

(x, y) = (2, 9), (3, 10), (4, 11)