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28 November, 11:44

at the end of her shift a cashier has a total of $6.30 in dimes and quarters. There are 7 more dimes than quarters. how many of each of these coins does she have?

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  1. 28 November, 12:07
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    The cashier has 23 dimes and 16 quarters.

    Step-by-step explanation:

    Let the amount of dimes = d.

    And the amount of quarters = q.

    We can write 2 equations with the given information.

    d = q + 7 - - - the amount of dimes is 7 more than the amount of quarters

    0.1d + 0.25q = 6.3 - - - a dime is 0.1 dollars and a quarter is 0.25 dollars

    0.1 (q + 7) + 0.25q = 6.3 - - - we can substitute q + 7 for d because they have the same value and we need to have only 1 variable to solve

    0.1q + 0.7 + 0.25q = 6.3 - - - distribute multipliers outside the parenthesis

    0.35q + 0.7 = 6.3 - - - combine like terms

    0.35q = 5.6 - - - subtract 0.7 from both sides

    q = 16 - - - divide both sides by 0.35

    The cashier has 16 quarters. We can use this to solve for dimes.

    d = q + 7

    d = 16 + 7

    d = 23

    The cashier has 23 dimes and 16 quarters.

    0.1d + 0.25q = 6.3

    0.1 (23) + 0.25 (16) = 6.3

    2.3 + 4 = 6.3

    6.3 = 6.3

    The answer is correct.
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