Question

Mahdi’s test grades in History class are: 92, 89, 85, 89, and 90. The semester final will count as two tests. Mahdi needs to get a grade of 90 or higher for the semester. What is the minimum score Mahdi can get on the final test and average 90?

Answer 1

The formula to calculate an average score is the following

`A=\frac{\sum ^{}_{}a_i}{n}`

where ai represents each individual grade, and n the number of values

Mahdi already has 5 grades: 92, 89, 85, 89 and 90

He will take a test that counts as 2, therefore the number of values will be 7

Since he needs to get a grade of 90 or higher for the semester, A = 90

Let's replace the above

`90=(92+89+85+89+90+2F)/(7)`

where F is his grade on the final exam, which is worth double

Now, let's solve for F. I will show you the steps:

`(92+89+85+89+90+2F)/(7)=90`
`(7\left(92+89+85+89+90+2F\right))/(7)=90\cdot\: 7`
`445+2F=630`
`2F+445-445=630-445`
`2F=185`
`(2F)/(2)=(185)/(2)`
`F=(185)/(2)`

Thus, the minimum score must be at least 92.5