Final answer:
It is not possible to buy the necessary 150 beads and string with a budget of $7.00 when the string costs $1.50, decorative beads cost $0.50 for a pack of 10, and plain beads cost $5.75 for a pack of 25.
Step-by-step explanation:
The student is tasked with purchasing beads and string to make a necklace and must adhere to a budget of $7.00. The string costs $1.50, and the bead packages cost $0.50 for 10 decorative beads and $5.75 for 25 plain beads. A total of 150 beads is required to make the necklace. To solve this, first, subtract the cost of the string from the total budget: $7.00 - $1.50 = $5.50 remaining for beads.
Next, calculate the number of bead packages needed without considering the cost. Since the student needs 150 beads, and the packages come in 10 and 25 quantities, the student can buy no more than 5 packages of 10 beads (5 packages × 10 beads/package = 50 beads) and no more than 5 packages of 25 beads (5 packages × 25 beads/package = 125 beads), which total 175 beads, more than needed. The goal is to get as close as possible to 150 without going over.
To minimize cost, we prioritize the cheaper package of beads. If we purchase 5 packages of the decorative beads (50 beads) at $0.50 each, the cost is $2.50. Subtracting this from the remaining budget of $5.50 leaves us with $3.00. With $3.00, we can buy at most one package of plain beads, since they cost $5.75 each.
This gives us: 50 beads (decorative) + 25 beads (plain) = 75 beads total, which is only half of what is needed. Therefore, the student must buy all plain beads to meet the needed amount, which is 6 packages (6 × 25 beads/package = 150 beads) at a cost of $5.75 per package. Since buying 6 packages exceeds the remaining budget of $5.50, the student cannot afford all the required beads within the $7.00 limit. A
Therefore, the conclusion is that it's not possible to purchase 150 beads and the string within the $7.00 budget while using these options.