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?

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Answer 1 · 2016-11-10T14:34:10

The inequality that needs to be solved is: $\frac{3 t + 270}{6} \geq 90$ $(3t + 270)/6 >= 90$ .

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

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 $t$ $t$ then the sum of all the tests would be:

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

or

$270 + 3 t$ $270 + 3t$

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

$\frac{3 t + 270}{6}$ $(3t + 270)/6$

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

So the inequality that needs to be solved is:

$\frac{3 t + 270}{6} \geq 90$ $(3t + 270)/6 >= 90$

or

$\frac{t}{2} + 45 \geq 90$ $t/2 + 45 >= 90$

$\frac{t}{2} \geq 45$ $t/2 >= 45$

$t \geq 90$ $t >= 90$