AMC 10 Daily Practice Round 1

Complete problem set with solutions and individual problem pages

Problem 6 Easy

A batch of parts was to be processed by Alice and Bob in the ratio 8:5. Alice processed 1600 parts, which is 25\% more than her originally assigned amount. Bob completed only 60\% of the parts he was assigned. How many parts did Bob actually process?

  • A.

    480

  • B.

    600

  • C.

    500

  • D.

    720

  • E.

    800

Answer:A

To find how many parts Bob processed, we first calculate Alice's originally assigned number of parts. Since Alice processed 1600 parts, which is 25\% more than her assigned amount, we compute her original share as 1600 \div (1 + 25\%) = 1280 parts. Given the ratio 8:5, Bob's assigned share is 1280 \times \frac{5}{8} = 800 parts. Since Bob only completed 60\% of his assigned share, the actual number of parts Bob processed is 800 \times 60\% = 480 parts. Therefore, Bob processed 480 parts.