Mathematics

Question

Your piggy bank contains $19.75 in dimes and quarters. There are 100 coins in all. How many dimes are there?

2 Answer

  • Let x = be the number of dimes and y = number of quarters. 

    Since the total number of coins is 100, x + y = 100. 

    Since the total is cent value is 19.75, comprised of .10 for dimes and .25 for quarters, we have .10x + .25y = 19.75. 

    This is just a system of equations. Solve one of the dozen ways that work for solving systems of linear equations. 

    Using substitution: 

    x = 100 - y 

    Plug this into the other equation 

    .10 (100 - y) + .25 y = 19.75 

    10 - .10 y + .25 y = 19.75 

    10 + .15y = 19.75 

    .15 y = 9.75 

    y = 65 

    So there are 65 quarters. Since x + y = 100, there must be 35 dimes.
    Hope This Helps
  • d = no. of dimes
    q = no. of quarters

    $total equation
    .10d + .25q = 19.75

    No. of coins equation
    d + q = 100
    d = (100-q)

    Replace d
    with (100-q) in the $total equation
    .10(100-q) + .25q = 19.75
    10 - .10q + .25q = 19.75


    10.15 q = 9.75
    q = 
    q = 65 quarters

    100 - 65 =

    35 dimes.



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