Q17. - Algebra 1

Question

Bill's scores on his first four science tests are 86, 90, 84, and 91. What must Bill earn on the fifth test so that his average (mean) will be exactly 88?

Step-by-Step Solution

Answer

He should get 89 on the fifth test to get an average of 88.

Step 1. Write the formulae used.

The mean of a data is: 

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

Step 2. Write the given information.

The first four numbers in the data are 84, 86, 90 and 91.

The average of five numbers is 88.

Let the fifth number is x.

Step 3. DESCRIPTION OF STEP.

Use the formula of mean to find the fifth number, as

$$\begin{gathered} \text{ Mean}=\frac{84+86+90+91+x}{\text{5}} \\ 88=\frac{351+x}{5} \\ 88\times 5=351+x \\ x=440-351 \\ x=89 \end{gathered}$$

Thus, he should get 89 on the fifth test to get an average of 88.