Question

Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Write a system of linear inequalities to represent this situation, these are the answers: 2x + 3y < 18,1>0, and y > 0 23 + 3y > 18,3 > 0, and y> 0 O 2 + 3y 18,1 >0, and y > 0 23 + 3y > 18,5 > 0, and y > 0 3

Answer 1

Prices:

Fuel x: $2 per gallon

Fuel y: $3 per gallon

"You have at most $18 to spend on fuel" => This means that the sum of the partial costs (for x and y) should be less than or equal to $18. If we have x gallons of fuel x, and y gallons of fuel y, then:

Cost for x: 2x

Cost for y: 3y

The linear inequality is:

`2x+3y\le18`

Since x and y are the numbers of gallons of fuel x and y, respectively, they must be positive (or zero). Then, the system of linear inequalities is:

`\begin{cases}2x+3y\le18 \\ x\ge0\text{ and }y\ge0\end{cases}`