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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?

Respuesta :

Edufirst
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
lhmarianateixeira

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

[tex]C=16[/tex]

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

  • Number of trumpets: t
  • Number of clarinets: c
  • Sold a total of 27 used trumpets and clarinet
  • Trumpets cost $149 and clarinets cost $99
  • Total sales were $3223

With this information we can assemble the equations as:

[tex]t + c = 27\\149t + 99c = 3223[/tex]

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

[tex]149t + 149c = 4023\\149c - 99c = 4023 - 3223\\50c = 800\\c = 800 / 50 \\c=16[/tex]

See more about system at brainly.com/question/7589753

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