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Math Help - Schillings

  1. #1
    Member Rimas's Avatar
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    Schillings

    Herr Vitami buys three kinds of frut for 40 schillings,10schillings and 1 schilling each. He pays 259 schilling for 100 peices of fruit. How many of the cheapest type of fruit did he buy?
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  2. #2
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    Hello, Rimas!

    Herr Vitami buys three kinds of frut for 40 shillings,10 shillings and 1 shilling each.
    He pays 259 shillings for 100 peices of fruit.
    How many of the cheapest type of fruit did he buy?

    Let A = number of 40-shilling fruit.
    Let B = number of 10-shilling fruit.
    Let C = number of 1-shilling fruit.
    . . Note: A,\,B,\,C are positive integers.

    He bought 100 pieces of fruit: . . (1)\;\;A + B + C \:=\:100

    He paid 259 shillings for them: . (2)\;\;40A + 10B + C \:=\:259

    Subtract (1) from (2): . 39A + 9B\:=\:159\quad\Rightarrow\quad 13A + 3B \:=\:53

    Solve for B\!:\;\;B \:=\:\frac{53-13A}{3}

    Since B is positive, there are only 4 choices for A\!:\:1,\,2,\,3,\,4

    . . \begin{array}{cccc}\text{If }A = 1,\;B = \frac{40}{3} \\<br />
\text{If }A = 2,\:B = \;9 \\ \text{If }A = 3,\:B = \frac{14}{3} \\ \text{If }A = 4,\:B = \frac{1}{3}\end{array}

    Hence: . A = 2,\:B = 9

    Therefore, from (1): . \boxed{C = 89}

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