Chapter 1.5, Problem 52HP

To determine

To find: the average of all 12 numbers.

Answer to Problem 52HP

  $8\frac{5}{12}$

Explanation of Solution

Given information:

The average of five numbers is 9, the average of 7 other number is 8.

Given option,

F. $8\frac{5}{12}$

G. $8\frac{7}{12}$

H. $8\frac{3}{4}$

J. $8\frac{11}{12}$

Calculation:

Let’s take twelve numbers and mark them from $x_1,x_2,\mathrm{...},x_{12}$

If the average of let’s say first five numbers is equal to 9, it can be written as:

  $\frac{x_1+x_2+x_3+x_4+x_5}{5}=9$

That means that sum of first five numbers is equal 46 which got by multiplying both sides of equation by 5.

Second part says that average of other seven numbers is equal 8, which means that

  $\frac{x_6+x_7+\mathrm{...}+x_{12}}{7}=8$

That means that sum of other seven numbers is equal 56 which got by multiplying both sides of equation by 7.

Now, if add those sums and divide them by 12, the average of all numbers,

  $\begin{array}{c}\frac{56+45}{12}=\frac{101}{12}\\ =8\frac{5}{12}\end{array}$

So, the average of all numbers is $8\frac{5}{12}$ .