If 3x + 5y = 10 and 5x + 3y = 30, what is the average (arithmetic mean) of x and y?

  1. 2.5
  2. 4
  3. 5
  4. 10
  5. 20
Explanation

Answer A

The average of x and y = (x+y)/2

If you add the two given equations, you find

3x + 5y = 10
5x + 3y = 30

8x +8y = 40
or x+y = 5

Hence average = 2.5

Key takeaway: One way may be to go for solving the two linear equations and find the variables. But that may be a longer rout. So always first look for any other way to attack such problems. Sometimes simply adding or subtracting the two equations may yield the desired result.

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