How many more students are needed to raise the average SAT score to 84?

[The_Journey]

Homework Statement

16 students took a test. Their average score was 77. At least how many more students must take the test to raise the average to up 84, if the maximum score possible on the test is 88?

Homework Equations

Average = Total / Number of people

The Attempt at a Solution

I have nowhere to start. Took a practice SAT and there were two of these problems and I'm really worried. I have a low GPA (3.9) and I need an asian score on the SAT to get into UCSD.

I tried doing 84 = Total score / Number of students but I'm stuck on the total score and number of students ?_?

 

[The_Journey]

Ok the answer is suppose to be 28. But how in the world did they get this??

 

[Mark44]

Let n = the number of additional students.

If 16 students took the test and got an average of 77 points, what was the total number of points?

For your second equation, you can assume that all n of the additional students get 88 points. You know what the average needs to be, and you can write an expression for the total score and for the number of people.
Average = Total/(No of people)

 

[snshusat161]

Let n = the number of additional students.

If 16 students took the test and got an average of 77 points, what was the total number of points?

For your second equation, you can assume that all n of the additional students get 88 points. You know what the average needs to be, and you can write an expression for the total score and for the number of people.
Average = Total/(No of people)

LOL, that's funny. We can't assume that all students will get 88. What you are saying is something like saying replace all students with more intelligent student's and average will go high upto 84. We have to take every student equal, at least as equal that 16 such student's will make only 77 as average.

 

[snshusat161]

Mark, I think you are right. I've thought for 10 to 15 minutes for this problem and could not find any reasonable clue for this problem.

 

[Mark44]

The key phrase is "At least how many more students must take the test ..." If you assume that some of the additional students get less than the max score, you will need more students.

 

[statdad]

Mark44 is correct. The fewest students required will occur if each scores the maximum possible score - that is why the information about the maximum score being 88 is provided.

Note: Journey, since you said "I need an asian score on the SAT" I would suggest there is more than your math/logic/thinking skills you need to improve before you head to college. What would have been wrong with saying "I need a high score"?

 

[ƒ(x)]

Note: Journey, since you said "I need an asian score on the SAT" I would suggest there is more than your math/logic/thinking skills you need to improve before you head to college. What would have been wrong with saying "I need a high score"?