The craft club is making bracelets and necklaces. It takes 25 beads to make a bracelet and 55 beads to make a necklace. The club has a maximum of 500 beads to use. Write a two-variable inequality to represent this situation. Is the point (−7,5)

Question

a viable solution? Why or why not?(1 point)
Responses

No, because this point is not within the solution set for the inequality.
No, because this point is not within the solution set for the inequality.

Yes, because the y-value is a positive whole number and the point is within the solution set.
Yes, because the y -value is a positive whole number and the point is within the solution set.

No, because while this point is within the solution set, −7
does not represent a viable value in this context.
No, because while this point is within the solution set, negative 7 does not represent a viable value in this context.

Yes, because both numbers are integers and thus fit the constraint against fractions or decimal values.

Answer 1

To represent the situation, let \( x \) be the number of bracelets and \( y \) be the number of necklaces. The total number of beads used can be expressed with the following inequality due to the constraints of the problem:

\[ 25x + 55y \leq 500 \]

Now, let's analyze the point \((-7, 5)\). Here, \(x = -7\) (which represents the number of bracelets), and \(y = 5\) (which represents the number of necklaces).

The reason why \((-7, 5)\) is not a viable solution is due to the fact that you cannot have a negative number of bracelets. In the context of this problem, both \(x\) and \(y\) must be non-negative integers (0 or greater) because you cannot create a negative number of bracelets or necklaces.

Thus, the appropriate response is:

No, because while this point is within the solution set, \(-7\) does not represent a viable value in this context.