Amusic 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?

In this exercise we will use the knowledge of finance in this way we have that:

First, we have to organize the information given in the statement as:

Number of trumpets: tNumber of clarinets: cSold a total of 27 used trumpets and clarinetTrumpets cost $149 and clarinets cost $99Total sales were $3223

With this information we can assemble the equations as:

Now solving the equations to find the values of the unknowns we have that:

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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 they sold 16 clarinets