If the average (arithmetic mean) of x, y and 15 is 9, and the average of x, 2y and 2 is 7, then y =
Value of x
Use the following rule to set up algebraic expressions for the statements in the problem:
The average (arithmetic mean) of x, y, and 15 is , so if we know the average is 9, we can find the sum of those three values by multiplying the average by 3:
The second expression is the same. The average of x, 2y, and 2 is and if it equals 7, we can multiply the average by 3 to find the sum:
Finally, we can subtract these equations from each other to find y:
Alternatively, you can isolate a variable in one equation and plug it into the other. For example, x = 12 − y, and we can plug that into the second equation:
(12 − y) + 2y = 19.
12 + y = 19, and y = 7. The answer is (C).
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