# Marie scored 95, 86, and 89 on three science tests. She wants her average score for 6 tests to be at least 90. What inequality can you write to find the average scores that she get on her next three can tests to meet this goal?

Nov 10, 2016

The inequality that needs to be solved is: $\frac{3 t + 270}{6} \ge 90$.

She needs to average at least 90 on her three remaining tests to have at least a 90 overall average for all 6 tests.

#### Explanation:

To obtain an average you first add up all the scores of the tests and then divide by the number of tests.

So far Marie has taken 3 tests and we know the total number of tests will be 6 so we will be dividing by 6 to get the average of all the score.

If we let each of the three remaining tests each be represent by $t$ then the sum of all the tests would be:

$95 + 86 + 89 + t + t + t$

or

$270 + 3 t$

The average of these 6 tests can then be represented by:

$\frac{3 t + 270}{6}$

And for her average to be at least 90 then she can get a 90 or more which is the same as $\ge 90$

So the inequality that needs to be solved is:

$\frac{3 t + 270}{6} \ge 90$

or

$\frac{t}{2} + 45 \ge 90$

$\frac{t}{2} \ge 45$

$t \ge 90$