# Jane has scored the following marks on the first 5 exams: 65, 70, 55, 87, 87. What is the minimum score she must achieve on the last exam if she is to reach her target of a 70% average?

Sep 20, 2017

$61$

#### Explanation:

$\text{Sum of the scores of 5 exams} = 65 + 70 + 55 + 82 + 87 = 359$

"Average of 6 exams" = ("sum of 5 exams" + x) / 6

where $x$ is the min. score required in exam $6$.

$70 = \frac{359 + x}{6}$

$6 \cdot 70 = 359 + x$

$420 = 359 + x$

$x = 420 - 359$

$x = 61$

So $61$ is the min mark required in exam $6$ for a final grade of C.

Sep 20, 2017

She needs at least $61$ in the sixth exam.

#### Explanation:

$\text{Mean" = "Total"/"Number}$

From this we can calculate the $\text{Total}$ by multiplying:

$\text{Total" ="Mean"xx"Number}$

If the average for $6$ exams must be $70$, the total for all $6$ exams must be:

$T = 6 \times 70 = 420$

Jane's total after $5$ exams is: $60 + 70 + 55 + 82 + 87 = 359$

Therefore in the last exam she should score a mark of at least:

$420 - 359 = 61$

$\frac{60 + 70 + 55 + 82 + 87 + 61}{6} = 70$