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29 May, 19:07

Sierra has a total of 61 dimes and quarters in her piggybank. She has 3 more quarters than dimes. The coins have a total value $10.90. How many dimes and how many quarters does she have? [hint: use the decimal values of the c coins to write an equation.]

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  1. 29 May, 19:29
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    Since you have two unknowns, you must formulate 2 equations in order to solve the system. Let x be the numbers of dimes and y be the number of quarters. The equations are:

    x + y = 61

    y = x + 3

    Since a dime is 1/10 of a dollar and a quarter is 1/4 of a dollar,

    (1/10) x + (1/4) y = 10.90

    We made 3 equations. The system is overspecified. Let's just use the first two equations and apply it to the third for verification.

    x + (x + 3) = 61

    Solving for x,

    x = 29

    y = 29 + 3 = 32

    Verifying,

    (1/10) (29) + (1/4) (32) = 10.90

    Hence, there are 29 dimes and 32 quarters.
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