AMC 10 Weekly Practice Round 2

Complete problem set with solutions and individual problem pages

Problem 27 Medium

Liam is processing a batch of parts. If he makes 50 parts per day, he will finish 8 days later than originally planned. If he makes 60 parts per day, he will finish 5 days earlier than originally planned. How many parts are in this batch?

  • A.

    3500

  • B.

    3600

  • C.

    3700

  • D.

    3800

  • E.

    3900

Answer:E

Let the originally planned production time be x days, and let the total number of parts be y.

Then: (x + 8) \times 50 = y \quad (1)

(x - 5) \times 60 = y \quad (2)

From equation (2),

x = \frac{y}{60} + 5

Substituting into equation (1) gives:\left( \frac{y}{60} + 5 + 8 \right) \times 50 = y

50y + 13 \times 50 \times 60 = 60y

y = 3900

Answer: The batch contains 3900 parts.

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