Percentage story problem

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R.Servant137

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Feb 28, 2010
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Gretel is in trouble in her history class. Her test scores so far have been 64%, 72%, 70%. There is only the final exam left to go, which will count the same as two tests. What grades could Gretel get on her final so that her average will be at least 80%? This should be solves as an inequality!
 
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If you had to average five numbers, how would you do it?

Three of these numbers (test scores) are given; the other two are unknown and equal.

In other words, the average of the five scores {64, 70, 72, x, x} needs to be greater than or equal to 80.

If you don't know how to express the average of these five numbers, let us know.

Otherwise, start solving the inequality for x the same way that you would if it were an equation. (Multiply both sides by the denominator, to get rid of the ratio.)
 
EG:

My course grade is the average of six test scores during the semester.

My first five scores are: {65, 69, 72, 61, 87}.

Let's say that I want to try get a course grade of 75. I've only got one test left to take, so what score do I need on my last test so that the average of all six numbers is at least 75?

We calculate the average (mean) of a set of numbers in two steps: (1) add the numbers together, and (2) divide their sum by their count.

In my example, I'm going to average six numbers; therefore, I divide their sum by six.

Here's how I write the inequality that says my average score is at least 75.

Let x = the unknown test score

\(\displaystyle \frac{65 + 69 + 72 + 61 + 87 + x}{6} \; \geq \; 75\)

Does this make sense?

Have you solved any inequalities? These simple types are solved very much like an equation.
 
It makes some sense, but I am still somewhat confused. I know the answer to my problem is 97%. Now how to get the answer is a different problem in itself. I have tried to use your layout of the inequality and I am unable to get the final answer of 97%. I have midterm tomorrow and somewhat nervous because of the story problems. I am pretty good at the others, but these silly story problems are "hurtin my brain" LOL!
 
R.Servant137 said:
I am unable to get the final answer of 97%.
Click to expand...

Okay. Let me work your exercise, to see what I get.

In the meantime, can you show me what you tried?
 
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If you would like to interact live, I'm currently at pathwhelp.org

Click on the [Live Help!] button.

Otherwise, multiply each side by 5, and simplify the LHS (lefthand side).
 
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