The school band bought a saxophone and a clarinet for $3314. The saxophone cost $2276 more than the clarinet.

What did each item cost?

If the clarinet's cost is c, then

c + c+2276 = 3314
2c = 1038
c = 519
and the sax cost 519 + 2276 = 2795

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Let's solve this problem step by step. Let's assume the cost of the clarinet as "x".

Since the saxophone cost $2276 more than the clarinet, the cost of the saxophone would be "x + $2276".

According to the problem, the total cost of the saxophone and the clarinet is $3314.

So, we can set up the following equation:
x + (x + $2276) = $3314

Simplifying the equation, we have:
2x + $2276 = $3314

Now, let's solve for x:
2x = $3314 - $2276
2x = $1038

Dividing both sides by 2, we get:
x = $1038 / 2
x = $519

Therefore, the clarinet costs $519 and the saxophone costs $2276 + $519 = $2795.

To solve this problem, you can set up a system of equations based on the given information.

Let's assume the cost of the clarinet is "x" dollars.
According to the given information, the saxophone cost $2276 more than the clarinet, so its cost would be "x + $2276".

The total cost of both instruments is $3314, so we can write an equation:
x + (x + $2276) = $3314

Simplifying the equation, we combine like terms:
2x + $2276 = $3314

Now, isolate the variable by subtracting $2276 from both sides:
2x = $3314 - $2276

Simplifying further, we get:
2x = $1038

Finally, divide both sides by 2 to solve for "x":
x = $1038 / 2

x = $519

Therefore, the clarinet costs $519, and the saxophone costs $2276 + $519 = $2795.