Answer :
Let's break down the problem step-by-step to find the correct inequality and possible values of [tex]\( y \)[/tex].
1. Identify the given information:
- Maximum amount Alina spent on gas: \[tex]$45. - Cost per gallon at the first gas station: \$[/tex]3.50.
- Cost per gallon at the second gas station: \[tex]$4.00. 2. Formulate the inequality: - Let \( x \) be the number of gallons bought at the first gas station. - Let \( y \) be the number of gallons bought at the second gas station. - The total amount spent on gas cannot exceed \$[/tex]45, so we can write the inequality as:
[tex]\[ 3.5x + 4y \leq 45 \][/tex]
3. Determine the possible values of [tex]\( y \)[/tex]:
- First, recognize that [tex]\( x \)[/tex] and [tex]\( y \)[/tex] must be non-negative since you can't buy a negative amount of gas:
[tex]\[ x \geq 0 \quad \text{and} \quad y \geq 0 \][/tex]
- To find the maximum value of [tex]\( y \)[/tex], consider the scenario where [tex]\( x = 0 \)[/tex]:
[tex]\[ 3.5(0) + 4y \leq 45 \implies 4y \leq 45 \implies y \leq \frac{45}{4} \implies y \leq 11.25 \][/tex]
- To find the minimum value of [tex]\( y \)[/tex], recognize again that y must be non-negative:
[tex]\[ y \geq 0 \][/tex]
Therefore, the inequality and the range of possible values of [tex]\( y \)[/tex] are:
[tex]\[ 3.5x + 4y \leq 45, \quad 0 \leq y \leq 11.25 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{3.5 x+4 y \leq 45,0 \leq y \leq 11.25} \][/tex]
1. Identify the given information:
- Maximum amount Alina spent on gas: \[tex]$45. - Cost per gallon at the first gas station: \$[/tex]3.50.
- Cost per gallon at the second gas station: \[tex]$4.00. 2. Formulate the inequality: - Let \( x \) be the number of gallons bought at the first gas station. - Let \( y \) be the number of gallons bought at the second gas station. - The total amount spent on gas cannot exceed \$[/tex]45, so we can write the inequality as:
[tex]\[ 3.5x + 4y \leq 45 \][/tex]
3. Determine the possible values of [tex]\( y \)[/tex]:
- First, recognize that [tex]\( x \)[/tex] and [tex]\( y \)[/tex] must be non-negative since you can't buy a negative amount of gas:
[tex]\[ x \geq 0 \quad \text{and} \quad y \geq 0 \][/tex]
- To find the maximum value of [tex]\( y \)[/tex], consider the scenario where [tex]\( x = 0 \)[/tex]:
[tex]\[ 3.5(0) + 4y \leq 45 \implies 4y \leq 45 \implies y \leq \frac{45}{4} \implies y \leq 11.25 \][/tex]
- To find the minimum value of [tex]\( y \)[/tex], recognize again that y must be non-negative:
[tex]\[ y \geq 0 \][/tex]
Therefore, the inequality and the range of possible values of [tex]\( y \)[/tex] are:
[tex]\[ 3.5x + 4y \leq 45, \quad 0 \leq y \leq 11.25 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{3.5 x+4 y \leq 45,0 \leq y \leq 11.25} \][/tex]
