Question

Sadie has x quarters and y dimes. She has at most 22 coins worth no less than $3.60 combined. Solve this system of inequalities graphically and determine one possible solution.

Answer 1

they are diffrent coins so that means theyy have diffrent valus.

Explanation:

Answer 2

Answer: y ≤ 22-x

Y ≥36 - 5/2x

Explanation:

VARIABLE DEFINITIONS:

X= the number of quarters

Y= the number of dimes

“at most 22 counc” -> 22 or fewer coins

Use the ≤ symbol

Therefore the total number of coins, x+ y, must be less than or equal to 22:

x+y ≤22

“no less than $3.60” -> 3.60 or more use the ≥ symbol

One quarter is worth $0.25, so x quarters are worth 0.25x. One dime is worth $0.10, so y dimes are worth 0.10y. The total 0.25x + 0.10y must be greater than or equal to $3.60:

0.25x+0.10y ≥3.60

Sole each inequality for y:

x+y ≤22 0.25x+0.10y ≥3.60

y ≤22-x 0.10y ≥3.60-0.25x

y ≥3.60-0.25x / 0.10

y ≥36-5/2x

Graph y ≤ 22 - x by shading down the graph

y ≥36 - 5/2x by shading up:

Since the point (16,2) is inside the double shaded region, one possible solution to the system of inequalities would be:

Sadie could have 16 quarters and 2 dimes