Question

Simon must maintain an average grade of 80% or better in his math class to be eligible to play sports. His math grades so far are: 80%, 84%, 76%, 77%. At this point, his grades make him ineligible to play. What is the lowest he score on his next grade to bring his average score up to an 80%. Part A: Write an inequality to represent the average of the five grades as greater than or equal to 80%. Part B: Use the inequality from Part A to prove what his lowest score could be on the 5th test.

Answer 1

Answer:

(a)[TeX]\frac{317+x}{5} $\geq$ 80[/TeX]

(b)83%

Step-by-step explanation:

His math grades so far are: 80%, 84%, 76%, 77%.

Let the lowest score required to bring his average score up to an 80% =x

(A)Average of the five scores

=[TeX]\frac{80+84+76+77+x}{5}[/TeX]

=[TeX]\frac{317+x}{5}[/TeX]

If the average of the five grades as greater than or equal to 80%.

Then:

[TeX]\frac{317+x}{5} $\geq$ 80[/TeX]

(b) To find what his lowest score should be, we solve the inequality derived in part A.

[TeX]\frac{317+x}{5} $\geq$ 80[/TeX]

Cross Multiplying

[TeX]317+x$\geq$ 5 X 80[/TeX]

[TeX]317+x$\geq$ 400[/TeX]

[TeX]x$\geq$ 400-317[/TeX]

[TeX]x$\geq$ 83[/TeX]

The lowest score he requires is 83%.