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The mean of 13, 17, and y is the same as the mean of 8, 14, and 3y. What is the value of y?

User Keynan
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1 Answer

3 votes

Answer:

y = 4

Explanation:

Defining the mean:

  • The mean is the average of a set of values.
  • We calculate it by dividing the sum of the values by the total number of values.

Mean of 13, 17, and y:

Since there are 3 values, the mean of the values is given by:

Mean 1 = (13 + 17 + y) / 3

Mean of 8, 14, and 3y:

Since there are 3 values, the mean of the values is given by:

Mean 2 = (8 + 14 + 3y) / 3

Now we can set the two means equal to each other and solve for y using the following steps:

Step 1: Combine like terms:

(30 + y) / 3 = (22 + 3y) / 3

Step 2: Multiply both sides by 3:

((30 + y) / 3 = (22 + 3y) / 3) * 3

30 + y = 22 + 3y

Step 3: Subtract 22 from both sides:

(30 + y = 22 + 3y) - 22

8 + y = 3y

Step 4: Subtract y from both sides:

(8 + y = 3y) - y

8 = 2y

Step 5: Divide both sides by 2 to solve for y:

(8 = 2y) / 2

4 = y

Thus, y = 4.

User Eekhoorn
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