To represent the given situation, we need to create a system of linear inequalities based on the given information. Let's break down the information we have: - Fuel x costs $2 per gallon. - Fuel y costs $3 per gallon. - We have at most $18 to spend on fuel. Now, let's consider the variables we'll use in our system of inequalities: - Let z represent the number of gallons of fuel x. - Let y represent the number of gallons of fuel y. To write the inequalities, we need to consider the cost constraint: - The cost of fuel x (2z) plus the cost of fuel y (3y) should be less than or equal to $18. So, the first inequality is: 2z + 3y ≤ 18 Next, let's consider the constraints on the variables: - We can't have a negative number of gallons for either fuel, so z and y should be greater than or equal to zero. So, the second inequality is: z ≥ 0 And the third inequality is: y ≥ 0 Combining these three inequalities, the correct system of linear inequalities to represent this situation is: 2z + 3y ≤ 18 z ≥ 0 y ≥ 0 Therefore, the correct answer is: 2z + 3y ≤ 18, z ≥ 0, and y ≥ 0.
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Answer:
[tex]2x+3y\leq 18,\;x\geq 0,\;\;\text{and}\;\;y\geq 0[/tex]
Step-by-step explanation:
Let x be the total number of gallons of fuel x.
Let y be the total number of gallons of fuel y.
If fuel x costs $2 per gallon, the total cost of fuel x can be represented by 2x.
If fuel y costs $3 per gallon, the total cost of fuel y can be represented by 3y.
Given that we have at most $18 to spend on fuel, we can sum the total cost of each fuel and set it to less than or equal to 18:
[tex]2x + 3y \leq 18[/tex]
Since we cannot purchase a negative amount of fuel, then the number of gallons of each fuel must be greater than or equal to zero:
[tex]x \geq 0[/tex]
[tex]y \geq 0[/tex]
So, the system of linear inequalities representing the situation is:
[tex]\begin{cases}2x+3y\leq 18\\x\geq 0\\y\geq 0\end{cases}[/tex]
