# Need help with seventh grade math?

There are 76 seventh-graders, 38 eighth-graders, and 58 sixth-graders. There are 35 students on student council. Determine a fair number of students to represent each grade on the student council. How would the number of students from each grade change if the number was changed from 35 to 37?

Relevance

It's a proportion problem.

Get the total number of students, divide by the number of representatives. That gives you the number of students represented by each council member. (A bit less than 5)

Divide the number of kids per class by that number, that will give you the number of reps per class.

Of course you can not have fractional reps or kids, so thats where you'have to round up-- or down fairly to get whole numbers-- or justify the older kids having an extra rep,, because of their seniority, expertise, whatever.

Have fun!

• So you want to turn everything into percentages. First find out total number of students 76+38+58=172. Then find out percentage for each class 76/ 172 for seventh graders , 38/172 for eighth graders, and 58/172 for sixth graders. Once you have that you will multiple each of those percentages by your 35 to get the number of students from each grade that can be represented in the student council. For 37 you would replace the 35 with the 37 in the fInal step

• How many total students are there?

What proportion (percentage) are in each grade?

Multiply each grade's proportion by the number of students on the council; that's their fair (per-capita) representation.

For instance, if we have 60% 7th graders and 20% in each of the other two classes, we get a representation of

35 * 0.60 = 21

35 * 0.20 = 7

35 * 0.20 = 7

... which is a total of 35 reps for the council.

See how it works?

By the way, the problem writer should be fired. A student council of 35 people isn't going to get anything reasonable done. Having 1/8 of the students on the council has far too many representatives, and the legislative logistics are not going to work with people at this level of training and maturity.

• First, let's get the number of students. 76 + 38 + 58 = 172

Next, let's find what percentage of students those are. 76/172 = 0.44, so 44% are seventh graders. 38/172 = 0.22, so 22% are eighth graders. 58/172 = 0.34, so 34% are sixth graders.

To be fair, the student council should have about the same percentage of students. So 44% should be 7th graders, 22% should be 8th graders, and 34% should be 6th graders.

To change it to 37 members, just take 44% of 37, 22% of 37, and 34% of 37.

• Total students = 76 + 38 + 58 = 172

divide bythe number of council seats:

172/35 = 4.9 roughly 1 seat per 5 students

7th: 76/4.9 = 15.5

8th: 38/4.9 = 7.8

6th: 58/4.9 = 11.8

If these are rounded off they add to 36. The fairest thing to do is round down the 7th grade number (being the lowest fractional value), then they add up to 35. So 6th gets 12 seats, 7th gets 8, 8th gets 12 seats.

If the number on the council was 37:

172/37 = 4.65

6th: 58/4.65 = 12.47

7th: 76/4.65 = 16.34

8th: 38/4.65 = 8.17

The integer portions add up to 36. The extra should go to the class with the highest fractional number, the 6th grade. So 6th = 13, 7th = 16 and 8th = 8 seats.

- .--

• Add up all of the students to get a total number of students. 76+38+58.

Divide each group of students by total to get % each class has. Ex. 76 divided by total of students.

Now you have the % of each class.

Multiply % of class by 35 to find out how many each class should get. Ex. 35 X .44 = 15.4.

Don't forget to round off so you get whole numbers. You can not have 0.4 of a person.

Make sure that you don't end up with too many or too few people either. If you round off answers you should still end up with 35 total for all the classes.

Last do the % of each times 37 to get the answers for that part. Ex. 37 X .44= 16.28 or 16

Good luck.