Petra is making necklaces to sell at a craft fair. The hardware for each necklace cost 3.75, and each bead 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 correct expression to represent the total cost to make 30 necklaces, each using B beads, is: Total Cost=30(3.75+0.50B)\text{Total Cost} = 30(3.75 + 0.50B)
Explanation
Petra is preparing for a craft fair and plans to make and sell 30 necklaces. Each necklace consists of two components that affect the cost: the hardware and the beads.
- Cost of hardware per necklace: According to the information given, the hardware needed for each necklace costs $3.75. This cost remains constant for each necklace, regardless of the number of beads used.
- Cost per bead: Each bead costs $0.50. However, the number of beads used depends on the design Petra chooses, so the total bead cost for one necklace is $0.50 multiplied by B, where B represents the number of beads per necklace.
To find the cost to make one necklace, we add the hardware cost and the total bead cost: Cost of one necklace=3.75+0.50B\text{Cost of one necklace} = 3.75 + 0.50B
Since Petra is making 30 necklaces, we multiply the cost of one necklace by 30 to get the total cost for all necklaces: Total Cost=30×(3.75+0.50B)\text{Total Cost} = 30 \times (3.75 + 0.50B)
This expression allows Petra to calculate the total cost easily, even if she changes the number of beads in her design. For example, if she chooses to use 10 beads per necklace, she can substitute B = 10 into the expression and find the total cost as: 30(3.75+0.50×10)=30(3.75+5.00)=30×8.75=262.5030(3.75 + 0.50 \times 10) = 30(3.75 + 5.00) = 30 \times 8.75 = 262.50
Thus, the expression 30(3.75 + 0.50B) accurately models the total cost of producing the necklaces and reflects how both fixed and variable costs contribute to the final expense.
