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?
Answer
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
Explanation
The total cost is $3.50 for each of x gallons plus $4.00 for each of y gallons, so it is 3.5x + 4y. Since Alina spent no more than $45, 3.5x + 4y ≤ 45. Gallons cannot be negative, and the most she could spend on gas at the second station alone gives 45 ÷ 4 = 11.25 gallons, so 0 ≤ y ≤ 11.25. This matches choice C.
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