Thread: Averaging problem?

1. Averaging problem?

This is yet another problem on the sample 7th grade EOG test.

Shana and Mina are workign on a math project and will receive the same grade. Their individual grades before the project are listed below.

What grade could they receive that will keep Shana's average the same, but improve Mina's average by one point?

A) 83
B) 85
C) 87
D) 90

I worked this problem last night and I got D) 90, but I had to go thru all the possible answers before I got to the right answer. My question is, is there any short cut, or this the only way to solve a problem like this?

2. Originally Posted by cherryperry
This is yet another problem on the sample 7th grade EOG test.

Shana and Mina are workign on a math project and will receive the same grade. Their individual grades before the project are listed below.

What grade could they receive that will keep Shana's average the same, but improve Mina's average by one point?

A) 83
B) 85
C) 87
D) 90

I worked this problem last night and I got D) 90, but I had to go thru all the possible answers before I got to the right answer. My question is, is there any short cut, or this the only way to solve a problem like this?

_________________

I also have another problem that's similar, but I'm unable to figure it out:

Charlie and Daniel are playing darts. The winner will be the one wtih the highest average score after 6 games. Charlie ahs completed 6 games and has an average score of 190. So far, Daniel has played 5 games and has an average score of 183. What score does Daniel need in his final game to have the same average score as Charlie?

A) 190 points
B) 197 points
C) 225 points
D) 270 points

How do I begin to tackle this? I figure it's got to be simple b/c it's on a 7th grade test. I think?
Hi Cherry,

yes, there is a fast way to get the first one.

Calculate Shana's average, which is 450/5=90

In order to keep her average the same, she needs a 90
as below 90 will drop her average and above 90 will raise it.

Apparently that will necessarily raise Mina's average by 1,
so that information was in fact irrelevant as only 90 will keep Shana's average steady.

For 2) you need $\displaystyle \frac{183(5)+x}{6}=190$

3. Thanks, Archie! Wow, that sure does simply things!

Can you tell me how to go about solving this one?

Charlie and Daniel are playing darts. The winner will be the one withh the highest average score after 6 games. Charlie has completed 6 games and has an average score of 190. So far, Daniel has played 5 games and has an average score of 183. What score does Daniel need in his final game to have the same average score as Charlie?

A) 190 points
B) 197 points
C) 225 points
D) 270 points

How do I begin to tackle this?

Edited to correct spelling.

4. Originally Posted by cherryperry
Thanks, Archie! Wow, that sure does simply things!

Can you tell me how to go about solving this one?

Charlie and Daniel are playing darts. The winner will be the one withh the highest average score after 6 games. Charlie has completed 6 games and has an average score of 190. So far, Daniel has played 5 games and has an average score of 183. What score does Daniel need in his final game to have the same average score as Charlie?

A) 190 points
B) 197 points
C) 225 points
D) 270 points

How do I begin to tackle this?

Edited to correct spelling.
Yes,

Daniel's average of 183 is his first 5 scores added together and divided by 5.
Therefore the sum of his first 5 scores is 5(183).

The average of his entire 6 scores will be the sum of the first 5 plus his final score.
We can call the final score x.

Then, after 6 rounds his average is

$\displaystyle \frac{sum\ of\ 6\ scores}{6}=\frac{sum\ of\ first\ 5\ scores+final\ score}{6}=\frac{5(183)+x}{6}$

and this needs to be 190

$\displaystyle \frac{5(183)+x}{6}=190$

$\displaystyle 5(183)+x=6(190)$

$\displaystyle 915+x=1140$

$\displaystyle x=1140-915$