Answer:
The possible solution is:
(10,2)
Step-by-step explanation:
Gas costs $3 per gallon and diesel costs $5 per gallon.
You have at most $43 to spend on fuel.
You must purchase at least 8 gallons of gas for your car to run for the week.
Let x be the amount of gas purchased and y be the amount of diesel purchased.
Hence, the system of inequalities that are obtained on the basis of above information is:
[tex]x\geq 8------(1)[/tex]
and [tex]3x+5y\leq 43-------(2)[/tex]
Hence, we will check which options will lie in the feasible region formed by the following inequalities.
1)
(10,8)
As this inequality will not satisfy the second inequality.
( since 3x+5y=30+40=70 which is not less than 43)
Hence, option 1 is incorrect.
2)
(10,-8)
This is not a desirable quantity,.
Since the quantity of diesel can't be negative.
3)
(2,10)
This ordered pair do not satisfy inequality (2).
Hence, option 3 is incorrect.
so, the possible solution is:
(10,2)
