Inequalities with Context

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

I. x+y < 15

II. 5x + 10y > 100 divide by 5

x + 2y > 20

III. x< 4

IV. y > 11

inequalities I,III and IV create a solution set that is a right triangle with vertices (4,11), (0,11) and (0,15) inequality II is redundant and does not change the solution.

possible solutions are:

x=nickels y = dimes

4 11

3 11 or 12

2 11, 12 or 13

1 11, 12, 13, or 14

0 11, 12, 13, 14 or 15

15 different possibilities