Q56. - Algebra 1

Question

Devonte's scores on his first four Spanish tests are 92, 85, 90, and 92. What test score must Devonte earn on the fifth test so that the mean will be exactly 90?

Step-by-Step Solution

Answer

Devonte’s score in the fifth test should be 91 so the mean is 90.

Step-1. Apply the concept of the mean.

Mean is the average of all the observations 

$\text{Mean = }\frac{\text{Sum of all the observations}}{\text{Total number of observations}}$

Step-2. Evaluate the given data.

Let Devonte’s score in the fifth test is x

Given scores in four tests:

92, 85, 90, and 92

The mean of scores of five tests is 90

Step-3. Calculation of score.

Substituting all the values from step 2 in the mean formula:

$\begin{array}{l}\text{Mean = }\frac{\text{Sum of all the observations}}{\text{Total number of observations}}\\ \Rightarrow 90=\frac{92+85+90+92+x}{5}\\ \Rightarrow \frac{359+x}{5}=90\\ \Rightarrow 356+x=\mathrm{450.........................}[\text{multiply each side by 5]}\\ \Rightarrow x=450-\mathrm{359.........................}[\text{subtract 365 from each side]}\\ \Rightarrow x=91\end{array}$

So, Devonte’s score in the fifth test should be 91 so that the mean is 90.