# the geometric mean of the first two tests as their official score. Larissa scored 91% on the first test, 71% on the second test, and 80%?

## Students in Mrs. Hoyt's math class have taken three tests so far. For their third test, they can choose to use the score they received on the test, the average score of the first two tests, or the geometric mean of the first two tests as their official score. Larissa scored 91% on the first test, 71% on the second test, and 80% on the third test. Which scoring option should she choose?

Feb 28, 2018

See a solution process below:

#### Explanation:

Score Larissa had on the third test: $80$

Average score of first two tests:

$\frac{91 + 71}{2} = 81$

Geometric Mean of first two tests:

• First Multiply the two scores: $91 \cdot 71 = 6461$

• Then, because there are two scores, take the square root:

$\sqrt{6461} = 80.38$

If Larissa wants the highest score possible she should choose the Average score of the first two tests

Feb 28, 2018

Larissa should choose the average of average score of the first two tests.

#### Explanation:

Let's do each of the options one at a time and see how they compare.
We know that 80% is how much she scored on her third test, so that is the first option.
The average of her first two tests formula would be $\frac{91 + 71}{2}$ $\rightarrow$ $\frac{162}{2}$ then divide it to become 81%
The geometric mean formula of of the first two tests is $\sqrt{91 \times 71}$ $\rightarrow$ $\sqrt{6461}$ and then find the square (with a calculator) which is $\approx$ 80.38%

The best option is 81%, which the average score of her first two tests.