quizzes are , , and . Determine in terms of an inequality what scores on the last quiz will allow her to get an average of at least ?

Question

 Tiffany's quiz grades on the first four quizzes are , , and . Determine in terms of an inequality what scores on the last quiz will allow her to get an average of at least ?

Answer 1

You said there were already four quizzes, and you want to know the constraints on the fifth. But the problem description only has room for three. (By the way, did you know that the scores on the quizzes didn’t get into your post? Nor the desired average.)

 

I’ll answer it for four quizzes plus a final fifth quiz. You should be able to change it in case there’s a different number.

 

Fitst identify the quantities involved.

Let v be the First score

Let w be the second score

Let x be the third score

Let y be the fourth score

Let z be the upcoming final quiz that you’re curious about

Let a be the desired average

 

Next write an equation (or inequality) relating them:

Do you know how to compute an average? It’s the sum of the numbers divided by the number of numbers.

 

So your inequality begins its life this way:

(v+w+x+y+z)/5 > a

 

Does that make sense? You want the average to be greater than a.

 

Now the only unknown here is z, the score she needs to get on the last quiz, so we need to solve for z. It’s just like solving an equation, except that if you multiply both sides by a negative number, you have to swap the sign. We won’t be doing that, so here goes:

(v+w+x+y+z)/5 > a

multiply both sides by 5

(v+w+x+y+z) > 5a

subtract the known scores from both sides

z > 5a - v - w - x - y

 

That’s the inequality you seek. Fill in the scores on the first four quizzes, and fill in the desired average (a), and do the math.