Q19. - Algebra 1

Question

Olivia has an average score of 92 on five French tests. If she earns a score of 96 on the sixth test, what will her new average score be?

Step-by-Step Solution

Answer

The average of scores in 6 tests is equals to 92.66

Step 1. Write the formulae used.

The average/mean of a data is:

Step 2. Write the given information.

The average of 5 of Olivia’s tests is 92.

The score in the 6th test is 96.

Let the sum of the score of 5 tests be x.

Step 3. Description of step.

First use the formula of mean to find the sum of scores of 5 tests as:

$$\begin{gathered} \text{Average}=\frac{x}{\text{5}} \\ 92=\frac{x}{5} \\ 92\times 5=x \\ x=460 \end{gathered}$$

Thus, the sum of scores of 5 tests is 460.

Now again use the formula of average to find the average of 6 tests as:

$$\begin{gathered} \text{Average}=\frac{\text{sum of scores in 5 tests}+{\text{score in 6}}^{th}\text{ test}}{6} \\ =\frac{460+96}{6} \\ =\frac{556}{6} \\ =\frac{278}{3} \end{gathered}$$

Thus, the average of scores in 6 tests equals to $\frac{278}{3}=92.66$.