Question

John's math course requires 5 tests. His first 4 grades were 95, 72, 83, and 86.To end up with an average score of at least 84.6, what is the lowest score John will need on the fifth test?

Answer 1

We need that the average is at least 84.6 points. Let x be the score of the final test, the average then will be:

`(95+72+83+86+x)/(5)=(x+336)/(5)`

And we need this to be at least 84.6, this can be written as:

`(x+336)/(5)\ge84.6`

Now we solve this inequality to find x:

`\begin{gathered} (x+336)/(5)\ge84.6 \\ x+336\ge84.6\cdot5 \\ x+336\ge423 \\ x\ge423-336 \\ x\ge87 \end{gathered}`

Therefore John has to achieve at least 87 points in the fifth test to achieve an average of 84.6.