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

1. Problem Description

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

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0. Clarinets cost $55 each, and trumpets cost $96.80 each. We are asked to formulate a system of linear equations that can be used to find the number of clarinets (C) and trumpets (T) sold, but we are not required to solve the system.

2. Solution Steps

Let $C$ represent the number of clarinets sold and $T$ represent the number of trumpets sold.

The total number of instruments sold is 37, so we can write the first equation as:

$C + T = 37$

The total cost of the instruments is $2703.

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0. The cost of clarinets is $55C$ and the cost of trumpets is $96.80T$. So we can write the second equation as:

$55C + 96.80T = 2703.80$

Therefore, the system of linear equations is:

$C + T = 37$

$55C + 96.80T = 2703.80$

3. Final Answer

The system of linear equations from which $C$ and $T$ may be found is:

$C + T = 37$

$55C + 96.80T = 2703.80$