Question

In his algebra class, Rob has scores of 79, 85, 81, and 65 on his first four tests. To get a grade of C, the average of the first five tests must be greater than or equal to 70 and less than 80. Solve an inequality to find the range of scores that Rob can earn on the fifth test to get a C.

Answer 1

Rob score must be greater than or equal to 40 or less than 90 to get a grade of C.

Explanation:

We are given the following in he question:

Marks of 4 test: 79, 85, 81, 65

Let x be the marks obtained in the fifth test.

`\text{Average} = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

The average of the first five tests must be greater than or equal to 70 and less than 80.

We can write this with the help of inequality:

`70 \leq \text{Average} < 80`

Putting the values, we get,

`70 \leq \displaystyle(79 + 85 + 81 +65 + x )/(5) < 80\\\\\Rightarrow 70 \leq \displaystyle(310 + x )/(5) < 80\\\\\Rightarrow 350 \leq 310 + x < 400\\\Rightarrow 40 \leq x < 90`

Thus, Rob score must be greater than or equal to 40 or less than 90 to get a grade of C.