Question

Chelsea uses blue and white beads to make bracelets. She uses twice as many blue beads (b) ( b ) as white beads (w) ( w ) and 30 to 36 total beads for each bracelet. The following system can be used to help determine the number of each bead color Chelsea uses.            b=2wb w≤36b w≥30                  b=2w  b w≤36  b w≥30   One of the system’s solutions is w=11.5 w = 11.5 and b=23 b = 23 . Explain this solution’s viability within the given context.

Answer 1

While the solution w = 11.5 and b = 23 mathematically satisfies the 2-to-1 ratio of blue to white beads, it is not feasible for making bracelets as beads cannot be in half units.

Step-by-step explanation:

Chelsea uses blue and white beads to make bracelets with a 2-to-1 ratio of blue beads (b) to white beads (w), with a total bead count ranging from 30 to 36 for each bracelet. The given system of equations and inequalities can be written as:

• b = 2w (there are twice as many blue beads as white beads)
• b + w ≤ 36 (the total number of beads must be less than or equal to 36)
• b + w ≥ 30 (the total number of beads must be at least 30)

Given the solution w = 11.5 and b = 23, we see that the number of blue beads is indeed twice the number of white beads. However, since bead count must be whole numbers, having half a bead (11.5) is not practical, thus this particular solution is not feasible in the real-world context of making bracelets.