(Linear System word problem) A total of 27 coins, in nickels and dimes, are in a wallet. If the coins total $2.15, how many of each t

Question

(Linear System word problem)
A total of 27 coins, in nickels and dimes, are in a wallet. If the coins total $2.15, how many of each type of coin are there?

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Vivian 6 days 2021-10-12T11:51:01+00:00 1 Answer 0

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    2021-10-12T11:52:40+00:00

    Answer:

    11 nickels and 16 dimes

    Step-by-step explanation:

    Let n and d represent the numbers of nickels and dimes respectively.

    As there are 27 coins, n + d = 27, which can be solved for d:  d = 27 – n.

    The total values of the coins are represented by:

    $0.05n + $0.10d = $2.15.  

    Substituting 27 – n for d, we get:

    0.05n + 0.10(27 – n) = 2.15 (which is entirely in the variable n).

    Performing the indicated multiplication, we get:

    0.05n + 2.7 – .10n = 2.15

    Next, we consolidate the n terms on the right side and the constants on the left:

    0.55 = 0.05n, or

    n = 0.55/0.05 = 11

    Thus, there are 11 nickels and 27 – 11, or 16, dimes.

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