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
2 answers:
Answer: y ≤ 22-x
Y ≥36 - 5/2x
Step-by-step 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
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