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

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

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.

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

Answer 1

To represent the situation with a two-variable inequality, we can define:

• Let \( x \) be the number of bracelets made.
• Let \( y \) be the number of necklaces made.

The inequality based on the beads needed for each item can be written as:

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

Now, let's analyze the point \( (-7, 5) \):

1. The \( x \)-coordinate is -7, which represents the number of bracelets. It is not possible to make a negative number of bracelets. Thus, this value does not make sense in this context.

2. The \( y \)-coordinate is 5, which represents the number of necklaces. This value is valid since it is a non-negative integer.

However, since \( x \) is negative, the point \( (-7, 5) \) does not represent a viable solution to the problem.

The correct interpretation is:

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