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27 August, 13:15

A collection of dimes and nickels has a total value of two dollars and contains 31 coins. How many dimes are there in the collection?

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  1. 27 August, 15:11
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    There are 9 dimes in this collection.

    Step-by-step explanation:

    Dimes are 10¢; nickels are 5¢.

    d + n = 31

    0.1d + 0.05n = 2

    In this system of equations, d represents the amount of dimes in this collection and n represents the amount of nickels in this collection.

    1. Isolate n in the first equation.

    n = - d + 31

    2. Substitute this value into the other equation to find the value of d.

    0.1d + 0.05 (-d + 31) = 2

    0.1d - 0.05d + 1.55 = 2

    0.05d + 1.55 = 2

    0.05d = 0.45

    d = 9

    If you'd like to know how many nickels are in the collection, just subtract the amount of dimes from the total number of coins in the collection.

    31 - 9 = 22
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