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.

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.

Answer 1

To set up the inequality for the craft club's situation, we define two variables:

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

According to the problem, making a bracelet requires 25 beads, and making a necklace requires 55 beads. The total number of beads used cannot exceed 500. Therefore, the inequality representing this situation can be written as:

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

Now, we need to determine whether the point \((-7, 5)\) is a viable solution. To do this, we can substitute \( x = -7 \) and \( y = 5 \) into the inequality:

\[ 25(-7) + 55(5) \leq 500 \] \[ -175 + 275 \leq 500 \] \[ 100 \leq 500 \]

This part is true, but we must also consider the context of the problem. Since \( x \) represents the number of bracelets and \( y \) represents the number of necklaces, both \( x \) and \( y \) must be non-negative integers (you cannot make a negative number of bracelets). The value \( x = -7 \) is negative and therefore not a valid solution in this context.

So the correct conclusion is:

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