Question

Adam has x x dimes and y y nickels. He has no less than 18 coins worth a maximum of $1.50 combined. Solve this system of inequalities graphically and determine one possible solution.

Answer 1

Since the point (2,12) is inside the double shaded region, one possible solution to the system of inequalities would be:

Sarah could have 2 nickels and 12 dimes.

Explanation:

Variable Definitions:

​ x = the number of nickels

y = the number of dimes

“a maximum of 18 coins" → 18 or fewer coins

Therefore the total number of coins, x + y, must be less than or equal to 18:

x + y ≤ 18

“no less than $1.20" → $1.20 or more

One nickel is worth $0.05, so x nickels are worth 0.05x. One dime is worth $0.10, so y dimes are worth 0.10y. The total 0.05x+0.10y must be greater than or equal to $1.20:

0.05x + 0.10y ≥ 1.20

Solve each inequality for y:

x + y ≤ 18 0.05x + 0.10y ≥ 1.20

y ≤ 18−x 0.10y ≥ 1.20 − 0.05x

y ≥ 1.20 - 0.05x / 0.10

y ≥ 12 − 1/2x

​Graph y ≤ 18 − x by shading down and graph y ≥ 12 − 1/2x by shading up: (png given)

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