Answer:
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.
Step-by-step 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)
Step-by-step explanation:
