Petra is making necklaces to sell at a craft fair. The hardware for each necklace costs
0.50. The number of beads Petra needs depends on the design she chooses. Which expression gives the total cost to make 30 necklaces with b beads?
The Correct Answer and Explanation is:
Correct Expression:
The expression that gives the total cost to make 30 necklaces with b beads per necklace, where each necklace has hardware costing $0.50, is: 30(0.50+b)30(0.50 + b)
Explanation
To calculate the total cost of making 30 necklaces, we must consider two components of the cost for each necklace:
- The cost of hardware, which is constant: $0.50 per necklace.
- The cost of beads, which depends on how many beads (denoted by bb) Petra uses in each necklace.
The problem does not state the price per bead, so it is assumed that each bead costs $1, or that “b” itself represents the total bead cost per necklace based on the design.
Step-by-step breakdown:
- Per necklace, the total cost is:
- Hardware: $0.50
- Beads: bb (could be the cost of beads or number of beads if each costs $1)
- Since Petra is making 30 necklaces, and the cost per necklace is 0.50+b0.50 + b, we multiply this expression by 30 to get the total cost for all necklaces: 30(0.50+b)30(0.50 + b)
This expression correctly combines the fixed cost of hardware and the variable cost of beads, then scales it up to account for 30 necklaces.
Why not other expressions?
- 0.50+30b0.50 + 30b is incorrect—it suggests only one hardware cost and 30 necklaces’ worth of beads.
- 30(0.50)+b30(0.50) + b is also incorrect—it adds the hardware cost for 30 necklaces, but only one set of beads.
- 30b+30×0.5030b + 30 \times 0.50 is mathematically equivalent to 30(0.50+b)30(0.50 + b), but less compact.
Thus, 30(0.50+b)\boxed{30(0.50 + b)} is the most accurate and simplified way to represent Petra’s total cost
.
