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Math Help - Marc and His Coins

  1. #1
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    Marc and His Coins

    Marc Bryan is putting P1 and P5 coins in his piggy bank. The total amount inside is P145. The number of P1 is 1 more than 3 times the number of P5 coins. How many P1 and P5 coins are there?
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  2. #2
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    Hello, magentarita!

    Marc Bryan is putting 1p and 5p coins in his piggy bank.
    The total amount inside is 145p.
    The number of 1p coins is 1 more than 3 times the number of 5p coins.
    How many 1p and 5p coins are there?

    Let x = number of 1p coins.
    Let y = number of 5p coins.

    We are told that: . x \:=\:3y+1 \quad\Rightarrow\quad x - 3y \:=\:1 .[1]

    The total value is: . 1\!\cdot\!x + 5\!\cdot\!y \:=\:145 \quad\Rightarrow\quad x + 5y \:=\:145 .[2]


    Subtract [1] from [2]: . 8y \:=\:144 \quad\Rightarrow\quad y \:=\:18

    Substitute into [1]: . x - 3(18) \:=\:1\quad\Rightarrow\quad x \:=\:55


    Answer: . \begin{Bmatrix}55\,\text{ 1p coins} \\ 18\,\text{ 5p coins} \end{Bmatrix}

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  3. #3
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    thanks

    Quote Originally Posted by Soroban View Post
    Hello, magentarita!


    Let x = number of 1p coins.
    Let y = number of 5p coins.

    We are told that: . x \:=\:3y+1 \quad\Rightarrow\quad x - 3y \:=\:1 .[1]

    The total value is: . 1\!\cdot\!x + 5\!\cdot\!y \:=\:145 \quad\Rightarrow\quad x + 5y \:=\:145 .[2]


    Subtract [1] from [2]: . 8y \:=\:144 \quad\Rightarrow\quad y \:=\:18

    Substitute into [1]: . x - 3(18) \:=\:1\quad\Rightarrow\quad x \:=\:55


    Answer: . \begin{Bmatrix}55\,\text{ 1p coins} \\ 18\,\text{ 5p coins} \end{Bmatrix}
    I like the way you set up equations from the given data in word problems.
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