Question

If the average of a, b and 9 is 13, what is the average of a + 5,5 – 2 and 3 ?
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Answer 1

Answer:

12

Step-by-step explanation:

It’s best to first look at what average actually means mathematically. When you take the average of something, you are simply adding up some number of data and dividing it by the number of data. My wording here may not be the best, but you could write it like this: average = (sum of data)/(number of data).

In this case, I would really like to treat these values like y values on an x, y graph.

For the first set then, we would have:

(1,a)

(2,b)

(3, 9)

This makes it easier to see that we have three data points. The average is 13 so the equation can be set up as follows:

(a+b+9)/3=13

In case your algebra is rough, here are the steps:

1. (a+b+9)/3*3=13*3

   a. (a+b+9)=39

2. a+b+9–9=39–9

   a. a+b=30

When you solve for this, you get a+b=30 and there is no use for simplifying this further.

Now we turn to what the average is of the new values. Again, I’m going to look at these like data points:

(1, a+5)

(2, b-2)

(3, 3)

You set up the equation the same,

Equation (I have put parentheses around the points just so that you can see them as separate numbers instead of random variables):

((a+5)+(b-2)+3)/3=average

Now this time we do not set this equal to an average because the average is our unknown. We just want to simplify this because we know that a+b=30.

Simplifying: (a+5+b-2+3)/3=(a+b+5–2+3)/3=(a+b+3+3)/3=(a+b+6)/3=(30+6)/3=(36/3)=12

12 is the answer.