Question

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. What is a possible solution? (10,8) (10, -8) (2,10) (10,2)

Answer 1

10,8 ????? I'm pretty sure

Answer 2

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:

$x\geq 8------(1)$

and $3x+5y\leq 43-------(2)$

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)