The problem describes a scenario where a musical supply store sells clarinets and trumpets. A school band orders 37 instruments in total. The total bill is $2703.80. A clarinet costs $55 and a trumpet costs $96.80. We need to write a system of linear equations that can be used to find the number of clarinets ($C$) and the number of trumpets ($T$) sold, but we are not asked to solve the system.

1. Problem Description

The problem describes a scenario where a musical supply store sells clarinets and trumpets. A school band orders 37 instruments in total. The total bill is $2703.

8

0. A clarinet costs $55 and a trumpet costs $96.

8

0. We need to write a system of linear equations that can be used to find the number of clarinets ($C$) and the number of trumpets ($T$) sold, but we are not asked to solve the system.

2. Solution Steps

Let $C$ be the number of clarinets sold, and let $T$ be the number of trumpets sold.

We can form two equations based on the given information:

* The total number of instruments is

3

7. This gives us our first equation:

$C + T = 37$

* The total cost of the instruments is $2703.

8

0. Since each clarinet costs $55 and each trumpet costs $96.80, we have:

$55C + 96.80T = 2703.80$

The system of linear equations is:

$C + T = 37$

$55C + 96.80T = 2703.80$

3. Final Answer

The system of linear equations is:

$C + T = 37$

$55C + 96.80T = 2703.80$