Answer
The system of linear inequalities include
2.25x + 2.45y ≤ 37
x + y ≤ 16.
The constraints include
x ≥ 0 and y ≥ 0
Step-by-step explanation
The fuel at ND Gas Station costs $2.25 per gallon and fuel at GT Gas Station costs $2.45 per gallon.
You have at most $37 to spend on gas from both or either of the stations. The car to be filled can hold a maximum of 16 gallons of fuel.
We are then instructed to write a system of linear inequalities to represent this situation and identify the constraints of the scenario.
Let the number of gallons of fuel that is bought at ND Gas Station be x.
Let the number of gallons of fuel that is bough at GT Gas Station be y.
The cost of x gallons of fuel from ND Gas Station = 2.25 × x = 2.25x dollars
The cost of y gallons of fuel from GT Gas Station = 2.45 × y = 2.45y dollars
But we know that the total amount spent on gas cannot be more than $37.
So,
2.25x + 2.45y ≤ 37
And we also know that the sum of the number of gallons bought from both stations cannot exceed 16 gallons.
x + y ≤ 16.
To note the constraints, we know that the number of gallons bought at each of the Gas Stations cannot be negative, so, the constraints will be that these are both greater than or equal to 0.
x ≥ 0
y ≥ 0
Hence, the system of linear inequalities include
2.25x + 2.45y ≤ 37
x + y ≤ 16.
The constraints include
x ≥ 0 and y ≥ 0
Hope this Helps!!!