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Math Help - quarters and dimes

  1. #1
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    quarters and dimes

    This is hard to visualize because quarters is 25 cents and dimes is 10 cents. I can't figure this out. Please help.

    A student has $6.80 in dimes and quarters. The number of dimes is two more than half the number of quarters. How many of each type of coin does the student have?

    Answer key: 22 quarters, 13 dimes

    Thanks.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by shenton View Post
    This is hard to visualize because quarters is 25 cents and dimes is 10 cents. I can't figure this out. Please help.

    A student has $6.80 in dimes and quarters. The number of dimes is two more than half the number of quarters. How many of each type of coin does the student have?

    Answer key: 22 quarters, 13 dimes

    Thanks.
    Translate into an equation. let x be the number of quarters, and the number of dimes is 2+x/2 then:

    680=25\,x+10\,(2+x/2).

    Now solve this for x which tells you the number of Q's, and from that the number of D's can be found.

    RonL
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  3. #3
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    Hello, shenton!

    If you're familiar with Systems of Equations, here's another approach.


    A student has $6.80 in dimes and quarters.
    The number of dimes is two more than half the number of quarters.
    How many of each type of coin does the student have?

    Answer key: 22 quarters, 13 dimes

    Let: \begin{array}{cc}D \:= & \text{number of dimes} \\ Q\:= & \text{number of quarters}\end{array}

    The D dimes are worth 10 each.
    . . Their value is: 10D cents.
    The Q quarters are worth 25 each.
    . . Their value is: 25Q cents.

    The total value of the coins is: . 10D + 25Q\:=\:680 (cents) [1]


    \underbrace{\text{The number of dimes}}\;\underbrace{\text{is}}\;\underbrace{\text  {two more than}}\;\underbrace{\text{half the number of quarters}}
    . . . . . . D\qquad\qquad\quad =\qquad\quad2\quad+\qquad\qquad\qquad\quad\frac{1}  {2}Q
    We have: . D\:=\:2 + \frac{1}{2}Q\quad\Rightarrow\quad 2D - Q\:=\:4 [2]


    Divide [1] by 5: . 2D + 5Q\:=\:136
    . . Subtract [2]: . 2D \,- \;Q \:= \;\;4

    And we have: . 6Q\,=\,132\quad\Rightarrow\quad\boxed{Q \,=\,22}

    Substitute into [2]: . 2D - 22 \:=\:4\quad\Rightarrow\quad\boxed{D\,=\,13}


    Therefore, there are 22 quarters and 13 dimes.

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