Write and solve an inequality to answer the question

Question

write and solve an inequality to answer the question if you have recieved scores of 10,8,9, and 7 on your quizes so far, on how many consecutive qizzes must you recieve a 10 before your quiz average is above 9?

Answer 1

First, let's find out how many quizzes you need to get a 10 on to bring your average score up to 9. We know that if you keep getting scores of 10, your average is only going to increase.

The average of the numbers given is (10 + 8 + 9 + 7)/4. But we want this average to equal 9 if we take x tests.

(10 + 8 + 9 + 7 + 10x)/(4+x) = 9

Simplifying gives:

(34 + 10x)/(4+x) = 9

(34 + 10x) = 9*(4+x)

34 + 10x = 36 + 9x

34 + x = 36

x = 2

We can confirm this is correct by finding what the average would be if you get a 10 on 2 quizzes.

Average = (10 + 8 + 9 + 7 + 10 + 10)/6 = 9

If we keep getting 10s, our average will increase. But to get an average of at least 9, you need to get a 10 on two quizzes.

Answer 2

(10 + 8 + 9 + 7 + 10x) / 14 > 9

34 + 10x > 126

10x > 92

x > 9.2

Answer 3

[10 + 8 + 9 + 7 + 10 * (x times of more quizzes)] / number of all quizzes > 9

[10 + 8 + 9 + 7 + 10x] / (x + 4) > 9

10x + 34 > 9x + 36

10x - 9x > 36 - 34

x > 2

you have to take at least 3 quizzes graded 10 to make your average above 9

Answer 4

We know that the average score is going to be the sum of all the scores, divided by how many quizzes you've taken.

So the average of the numbers given is (10 + 8 + 9 + 7)/4.

If you wanted to make your average at least 9, then let's find how many quizzes you need to get full credit on before you make your average 9. Of course, if you keep getting a perfect score, your average will just keep increasing.

But to make the average 9, let's say:

9 = (10 + 8 + 9 + 7 + (10*x))/(4+x), where x = the number of quizzes you have to take. In the numerator, we multiply it by 10 because that's the score we want on each of those quizzes.

Simplifying the numbers, we see:

9 = (34 + 10x)/(4+x)

We can multiply each side by 4+x and get:

9(4+x) = 34 + 10x

36 + 9x = 34 + 10x

We can combine like terms by subtracting 9x from each side now and subtracting 34 from each side too.

This leaves us with 2 = x.

We can double-check our work to see if scoring a 10 on 2 quizzes will give you an average of at least 9.

(10 + 8 + 9 + 7 + 10 + 10)/6 = 9.

In this way, we know you need to score 10 on at least 2 quizzes to get an average of 9 or higher.