A bag of coins contains only quarters and dimes. The number of dimes in the bag can be represented by x. The number of quarters is 6 more th

Question

A bag of coins contains only quarters and dimes. The number of dimes in the bag can be represented by x. The number of quarters is 6 more than twice the number of dimes. There are a total of 276 coins in the bag. What is x, the number of dimes in the bag?

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Nick 4 years 2021-08-26T12:51:45+00:00 1 Answers 8 views 0

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  1. Cherry
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    2021-08-26T12:53:30+00:00
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    Answer:

    There are 90 coins in the bag.

    Step-by-step explanation:

    Let x, y the number of dimes and quarters. Now we proceed to translate each relevant sentence into mathematical expressions:

    (i) The number of quarters is 6 more than twice the number of dimes:

    y = 2\cdot x + 6 (1)

    (ii) There are a total of 276 coins in the bag:

    x + y = 276 (2)

    By applying (1) in (2), we find that the number of dimes is:

    x+2\cdot x + 6 = 276

    3\cdot x = 270

    x = 90

    There are 90 coins in the bag.

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