Question

Brooke earned the following scores on four history tests: 88, 86, 92, and 84. Brooke wants to have an average score of at least 85 after the fifth test. Write and solve an inequality to find the possible scores that she can earn on her fifth test in order to meet her goal. The greatest score that she can earn on a test is 100. Is it possible for her to have an average score of 90 after the fifth test?

Do I do 85 ≤ (x + 350)/5?

Answer 1

Answer:

No

Step-by-step explanation:

for part B:

your last test would be 100 in order to see if it's possible to get a average of 90

So,

(88+86+92+84+100)/6

=75%

Therefore it is not possible

Answer 2

The inequality and the marks of the given situation is required.

The inequality is $\dfrac{x+350}{5}\geq 85$

Brooke needs to score at least 75 in the last test.

It would be possible to have an average score of 90 if Brooke scored 100 on the last test.

The total marks scored by Brooke is

$88+86+92+84=350$

Let $x$ be the number of marks scored in the last test

So, the average of the 5 tests will be

$\dfrac{x+350}{5}$

The average is at least 85, so

$\dfrac{x+350}{5}\geq 85\\\Rightarrow x+350\geq 425\\\Rightarrow x\geq 425-350\\\Rightarrow x\geq 75$

So, Brooke needs to score at least 75 in the last test.

If the average score is 90.

$\dfrac{x+350}{5}=90\\\Rightarrow x=5\times 90-350\\\Rightarrow x=100$

It would be possible to have an average score of 90 if Brooke scored 100 on the last test.

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