To represent the situation where the craft club is making bracelets and necklaces with a maximum of 500 beads, we can define two variables:
- Let \( x \) be the number of bracelets made.
- Let \( y \) be the number of necklaces made.
The inequality describing the maximum number of beads used is:
\[ 25x + 55y \leq 500 \]
Next, we evaluate whether the point \( (-7, 5) \) is a viable solution:
- The x-value (number of bracelets) is -7, which is not possible since you cannot make a negative number of bracelets.
- The y-value (number of necklaces) is 5, which is a positive whole number, but that does not make up for the fact that the x-value is negative.
Therefore, options regarding the point's viability are as follows:
- "Yes, because the y-value is a positive whole number and the point is within the solution set." is not correct.
- "Yes, because both numbers are integers and thus fit the constraint against fractions or decimal values." is not correct either.
- "No, because this point is not within the solution set for the inequality." is not quite accurate because it does not even fit the conditions of the problem.
- "No, because while this point is within the solution set, -7 does not represent a viable value in this context." is the most appropriate explanation.
The correct response is: No, because while this point is within the solution set, -7 does not represent a viable value in this context.
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