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17 January, 23:03

A music store sold a total of 27 used trumpets and clarinets in one month. Trumpets cost $149 and clarinets cost $99. If total sales were $3223, how many clarinets did they sell?

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  1. 17 January, 23:22
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    Answer: 16

    Solution:

    1) Use letters to identify the variables:

    Number of trumpets: t

    Number of clarinets: c

    2) Translate each statement into algebraic (mathematical) language.

    2.1) Sold a total of 27 used trumpets and clarinets

    => t + c = 27

    2.2) Trumpets cost $149 and clarinets cost $99

    Total cost of the trumpets: 149t

    Total cost of clarinets: 99c

    Total cost = 149t + 99c

    2.3) Total sales were $3223

    => 149t + 99c = 3223.

    3) State the system of equations:

    Equation (1) t + c = 27

    Equation (2) 149t + 99c = 3223

    4) Solve the system of equations:

    4.1) Multiply equation 1 by 149:

    => 149t + 149c = 4023

    4.2) Subtract the equation (2) from the equation obtained in 4.1

    => 149c - 99c = 4023 - 3223

    => 50c = 800

    => c = 800 / 50 = 16

    5) Verify the solution:

    From equation (1) t = 27 - 16 = 11

    Total cost = 149*11 + 99*16 = 3223

    Now you have a verified answer: they sold 16 clarinets
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