Question

1**. Ms. Syed has an average of 91% on 5 assignments in her math class. Ms. Crockett has gotten a 91%, 70%, 99%, 81% on the first four assignments. If Ms. Crockett really wants to have a higher grade than Ms. Syed, what will she need to score on the next assignment in order to beat Ms. Syed's average? Mathematically speaking, will she be able to do it?

Answer 1

Given:

Total number of asignments, N=5

Average of Syed on 5 assignments, A=91%.

Ms. Crockett has gotten a 91%, 70%, 99%, 81% on the first four assignments.

Let a be the average of Ms. Crockett.

Let x be the grade got by Ms. Crockett on the fifth assignment.

Now, the average of Ms. Crockett can be expressed as,

$\begin{gathered} a=\frac{Total\text{ }}{\text{N}} \\ =\frac{91+70+99+81+x}{5} \\ a=\frac{341+x}{5} \end{gathered}$

Crockett has to get an average above 91% to beat Ms. Syed.

To find the score x, Ms. Crockett should get in the fifth assignment to beat Syed, put a=91% in the above equation.

$\begin{gathered} 91=\frac{341+x}{5} \\ 5\times91=341+x \\ 455=341+x \\ x=455-341 \\ x=114 \end{gathered}$

So, Ms. Crockett should get a score greater than 114% to overcome Ms. Syed's average.

But, it is mathematically impossible to get 114%. Hence, Ms. Crockett cannot beat Ms. Syed.