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27 July, 06:23

Russell ate several candies on Halloween, and each day after Halloween ate 6 fewer candies than the day before. His candies lasted exactly five days, and he ate 100 candies in total. How many did he eat on the third day?

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  1. K
    27 July, 07:42
    0
    Let a = the number of candies eaten on the first day.

    Because the number of candies eaten decreases by 6 every day after, the number of candies eaten creates the arithmetic sequence

    a, a-6, a-12, a-18, ...,

    After 5 days, the total candies eaten is 5a - 60.

    Therefore

    5a - 60 = 100

    5a = 160

    a = 32

    On the third day, the number of candies eaten is

    a - 12 = 32 - 12 = 20

    Answer: 20
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