Question

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Drew

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Answer

3.5x + 4y \leq 45 and 0 \leq y \leq 11.25.

Explanation

The problem describes a situation where Alina is spending money on gas for a road trip. The first gas station she used charged 3.50 per gallon, and the second gas station charged 4.00 per gallon. The total amount she spent on gas was no more than 45. This situation can be represented by the inequality 3.5x + 4y \leq 45, where x represents the number of gallons of gas she bought at the first station and y represents the number of gallons of gas she bought at the second station. To find the possible values of y, we need to solve the inequality for y\[\]. \[ \begin{align*} 3.5x + 4y &\leq 45 \\ 4y &\leq 45 - 3.5x \\ y &\leq \frac{45 - 3.5x}{4} \end{align*} \] Since x and y represent the number of gallons of gas, they must be non-negative (i.e., x \geq 0 and y \geq 0). Therefore, the possible values of y are between 0 and \frac{45 - 3.5x}{4}, inclusive. Looking at the options, the correct one is: 3.5x + 4y \leq 45 and 0 \leq y \leq 11.25. This means that the total amount Alina spent on gas is less than or equal to 45, and the number of gallons of gas she bought at the second station is between 0 and 11.25, inclusive.

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