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