Q18. - Algebra 1

Question

Bowling Sue's average for 9 games of bowling is 108. What is the lowest score she can receive for the tenth game to have an average of 110?

Step-by-Step Solution

Answer

The score in 10th game should be 128 to get an average of 10 games equals to 110.

Step 1. Write the formulae used.

The average/mean of a data is: 

$\text{Average}=\frac{\text{sum of all the numbers in data}}{\text{Total number of numbers in data}}$

Step 2. Write the given information.

The average of 9 games is 108.

The average of 10 games is 110.

Let the sum of the score of 9 games be x and let the score of 10th game be y.

Step 3. DESCRIPTION OF STEP.

First use the formula of mean to find the sum of scores of 9 games as

$$\begin{gathered} \text{Average}=\frac{x}{\text{9}} \\ 108=\frac{x}{9} \\ 108\times 9=x \\ x=972 \end{gathered}$$

Now again use the formula of mean to find the average of the score in the 10th game number, as:

$$\begin{gathered} \text{Average}=\frac{972+y}{\text{10}} \\ 110=\frac{972+y}{\text{10}} \\ 110\times 10=972+y \\ y=1100-972 \\ y=128 \end{gathered}$$

Thus, the score in the 10th game should be 128 to get an average of 10 games equals 110.