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.