Question

heidi's scores on her first 3 tests were 92, 95, and 86. what is the minimum score she mulst earn on her next test to maintain at least a 90 average

Answer 1

The inequality that needs to be solved is:

3t +270/ 6 ≥ 90.

let we consider that Heidi has 6 subjects in her school.

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

Now,

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

So far Heidi 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 + 92 + 86 + t + t + t

or

273 + 3t

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

3t + 273 / 6

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

So the inequality that needs to be solved is:

 $\frac{3t + 273}{6}$ ≥ 90

or, $\frac{3 ( t + 91)}{6} \geq 90$

or, $\frac{t + 91}{2} \geq 90$

Now, Heidi has to score :

t/2 ≥ 91

or, t/2 ≥ 90

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