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Math Help - coins/inequality word problem

  1. #1
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    coins/inequality word problem

    Bridgett has 64 coins in nickels and dimes. What is the minimum number of dimes she should have to have at least $4.55? Set up the inequality and solve.

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  2. #2
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    Hello, eunabug!

    Bridgett has 64 coins in nickels and dimes.
    What is the minimum number of dimes she should have to have at least $4.55?
    Set up the inequality and solve.

    Let: . \begin{bmatrix}n &=& \text{number of nickels} \\ d &=& \text{number of dimes}\end{bmatrix}

    Then: . n + d \:=\:64 \quad\Rightarrow\quad n \:=\:64-d .[1]

    The value of the coins is: . 5n + 10d cents
    . . which is to be at least 455 cents.

    We have: . 5n + 10d \:\ge \:455 .[2]


    Substitute [1] into [2]: . 5(64-d) + 10d \:\ge \:455

    . . 320 - 5d + 10d \:\ge \:455 \quad\Rightarrow\quad 5d \:\ge\:135  \quad\Rightarrow\quad d \:\ge\:27


    Therefore, Bridgett should have at least 27 dimes.
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