Question

Sally bought apples that cost $1.95 per pound and grapes that cost $2.59 per pound. The inequality 1.95 x + 2.59 y ≤ 15 can be used to show how many pounds of apples ( x )and how many pounds of grapes ( y ) Sally can buy if she wants to spend no more than $15.00. Which of the following values of x and y will satisfy the inequality and make sense for the problem?

A. x = − 2 , y = 7
B. x = − 1 , y = − 2
C. x = 2, y = 3
D. x = 6 ,

Answer 1

The valid combination of x and y from the provided options is C. x = 2, y = 3, which satisfies the inequality and makes sense within the context of the problem.

Step-by-step explanation:

When dealing with a problem like Sally buying apples and grapes, we use an inequality to determine the possible amounts of each fruit she can purchase without exceeding her budget. Here, we have the inequality 1.95x + 2.59y ≤ 15, where x represents the pounds of apples and y represents the pounds of grapes. Sally wants to spend no more than $15.00. So, we need to find the combinations of x and y that satisfy this condition.

Let's examine each pair of values to determine which one fits within Sally's budget constraint:

• A. x = -2, y = 7: This does not make sense, as negative quantities cannot represent physical amounts.
• B. x = -1, y = -2: Similarly, this option is invalid due to negative quantities.
• C. x = 2, y = 3: Plugging these values into the inequality gives us (1.95)(2) + (2.59)(3) = 3.90 + 7.77 = 11.67, which is less than 15. This is a valid solution and makes sense for the problem.
• D. x = 6, y is not given: Without a value for y, we cannot determine if this option satisfies the inequality.

Therefore, the only logical and valid pair from the options provided is C. x = 2, y = 3.