Alina spent no more than $45 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. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought at the second station, y, and the total amount she paid? What are the possible values of y? Answers: A) 3.5x + 4y ≥ 45, y ≥ 11.25 B) 3.5x + 4y ≥ 45, 0 ≤ y ≤ 10.375 C) 3.5x + 4y ≤ 45, 0 ≤ y ≤ 11.25 D) 3.5x + 4y ≤ 45, y ≥ 10.375
Alina spent no more than
3.50 per gallon and the second gas station charged $4.00 per gallon. Which inequality relates the number of gallons of gas she bought at the first station, x, the number of gallons of gas she bought at the second station, y, and the total amount she paid? What are the possible values of y? Answers: A) 3.5x + 4y ≥ 45, y ≥ 11.25 B) 3.5x + 4y ≥ 45, 0 ≤ y ≤ 10.375 C) 3.5x + 4y ≤ 45, 0 ≤ y ≤ 11.25 D) 3.5x + 4y ≤ 45, y ≥ 10.375
The Correct Answer and Explanation is:
Correct Answer: C) 3.5x + 4y ≤ 45, 0 ≤ y ≤ 11.25
Explanation:
Alina is taking a road trip and bought gas at two gas stations. The first station charges $3.50 per gallon, and the second charges $4.00 per gallon. She spent no more than $45 in total. Let:
- xx = gallons purchased at the first station
- yy = gallons purchased at the second station
The total cost of the gas she purchased is: 3.5x+4y3.5x + 4y
Because she spent no more than $45, this total must be less than or equal to 45: 3.5x+4y≤453.5x + 4y \leq 45
This inequality expresses the constraint on her total spending. Any solution (x,y)(x, y) that satisfies this inequality is a possible combination of gallons bought from both stations without exceeding her $45 budget.
Now, we determine the possible values of yy (gallons bought at the second station). Since gas at the second station costs more ($4.00), to find the maximum she could have bought there if she bought only from that station, set x=0x = 0: 3.5(0)+4y≤45⇒4y≤45⇒y≤454=11.253.5(0) + 4y \leq 45 \Rightarrow 4y \leq 45 \Rightarrow y \leq \frac{45}{4} = 11.25
This means the maximum value of yy is 11.25, and since she can’t buy negative gallons, the minimum is 0. So: 0≤y≤11.250 \leq y \leq 11.25
Why Option C is Correct:
- It correctly uses the inequality 3.5x+4y≤453.5x + 4y \leq 45 to reflect the budget limit.
- It correctly identifies the possible values of yy: from 0 to 11.25 gallons.
Why Other Options Are Incorrect:
- A and B use the wrong inequality sign (≥ 45), which contradicts “no more than $45.”
- D has the correct inequality but says y≥10.375y \geq 10.375, which wrongly restricts minimum y.
✅ Final Answer: C.
