Katie must take five exams in a math class. If her scores on the first four exams are 76, 74, 90, and 88, what score must Katie get on the fifth exam for her overall mean to be at least 80?

Feb 1, 2017

Her fifth exam's score must be 72 for her overall mean to be at least 80.

Explanation:

To get the overall mean, we should add all of the scores of her five exams and divide the sum by 5. This is represented in the following equation. "x" represents the fifth exam's score.
$\left(76 + 74 + 90 + 88 + x\right) \div 5 = 80$

Multiply both sides of the equation by 5 to get...
$76 + 74 + 90 + 88 + x = 400$.

Add all of the four given exam scores.
$328 + x = 400$

Then, subtract 328 from both sides of the equation to get...
$x = 72$.

Hope this helps you.

Feb 1, 2017

In the fifth test, Katie has to score at least $72$ for the purpose.

Explanation:

Suppose that a score of $x$ marks in the fifth exam yields Katie the

desired mean.

Then, the Mean score of all the tests$= \frac{76 + 74 + 90 + 88 + x}{5}$, and, as

this is reqd. to be at least $80$, we have,

$\frac{76 + 74 + 90 + 88 + x}{5} \ge 80$

$\Rightarrow \frac{328 + x}{5} \ge 80$

$\Rightarrow 328 + x \ge 5 \times 80 = 400$

$\Rightarrow x \ge 400 - 328 = 72$

So, in the fifth test, Katie has to score at least $72$ for the purpose.