Question

Katrina has scores of 74,83 and 86 after three tests her final exam counts as two test scores what score must she make on her final exam to have an average of 71 or greater?

Answer 1

Katrina makes four exams, but since the score she makes on last one counts as two, the formula of the average value would be like this:

`\text{Sav}=(s1+s2+s3+s4+s4)/(5)=(s1+s2+s3+2* s4)/(5)`

Now that we have the formula that relates the score of the last exam (s4) and the average score (sav), we can solve for s4, like this:

`\begin{gathered} sav=(s1+s2+s3+2* s4)/(5) \\ sav*5=(s1+s2+s3+2* s4)/(5)*5 \\ sav*5=s1+s2+s3+2* s4 \\ sav*5-s1-s2-s3=2* s4 \\ (sav*5-s1-s2-s3)/(2)=(2)/(2)* s4 \\ s4=(sav*5-s1-s2-s3)/(2) \end{gathered}`

Now, let's replace the known values so we can find the value of s4:

`\begin{gathered} s4=(71*5-74-83-86)/(2) \\ s4=(355-74-83-86)/(2)=(112)/(2)=56 \end{gathered}`

Then, Katrina must make more than 56 on the final test