Alice, Betty and Carol all have the same amount of money (more than 50 cents but less than a dollar). Alice has two coins, Betty and Carol e

Question

Alice, Betty and Carol all have the same amount of money (more than 50 cents but less than a dollar). Alice has two coins, Betty and Carol each have 3 coins, but Betty and Carol do not have any coins that are the same. How much money does each girl have?

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Samantha 4 months 2022-01-31T04:37:02+00:00 1 Answer 0 views 0

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    2022-01-31T04:38:58+00:00

    Answer:

    Each girl has 60 cents.

    Step-by-step explanation:

    Since they have between 50 cents and 1 dollar, then Alice should have a 50 cent coin and 1 coin of less value (because if she had 2 coins that are worth 25 cents or less, she would have only 50 cents at most).

    On the other hand, Both betty and carol need to have a coin that is at least 25 cents worth (because otherwise they would have 30 cents at most), but since they cant have the same coins, then one of them should have one 50 cent coin (and 2 small cent coins) and the other should have at least two twenty five cent coins.

    Lets assume that Betty has a 50 cent coin and Carol has two 25 cent coins. Since Alice also has a 50 cent coin, then the remaining coin of Alice should have the same value than the sum of the remaining 2 coins that Betty has.

    The values of the coins are 5,10, 25, 50, and 100. Since they cant have 1 dollar coins, then the only possibility for a coin to have the sum of the values of 2 coins is to have a value of 10 (10 = 5+5). Thus:

    • Alice has one coin of 50 cents and one coin of 10 cents
    • Betty has one coin of 50 cents and two coins of 5 cents
    • Carol has two coins of 25 cents and one coin of 10 cents

    Each girl has 50+10 = 50+5+5=25+25+10 = 60 cents

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