6.3+Selecting+Delegates+1011

January 10, 2011

JSP

Many important practical & mathematical applications involve comparing quantities of one kind or another; it is important to know which method to use & how we should use them.

Which comparing strategies work best in which situations?

Notes Vocabulary= proportion is a statement about equivalent ratios or fractions Example- ½ = 2/4 Method= using proportions. Like this- ½ = x/4 & I want to find x. I used this method to solve the problems in 6.3

**A.** **How many of the 1000 delegates should be chosen from each of the nine geographic regions?**
 * United States || 248,710 || 192,726 || 55,984 || 199,686 || 29,986 || 22,354 || 1959 || 7274 ||
 * New England || 13,207 || 10,598 || 2609 || 12,033 || 628 || 568 || 33 || 232 ||
 * Middle Atlantic || 37,602 || 34,193 || 3409 || 30,036 || 4986 || 3186 || 92 || 1104 ||
 * East North Central || 42,009 || 32,557 || 9452 || 35,764 || 4817 || 1438 || 150 || 573 ||
 * West North Central || 17,660 || 10,132 || 7528 || 16,254 || 899 || 289 || 188 || 195 ||
 * South Atlantic || 43,567 || 32,461 || 11,106 || 33,391 || 8924 || 2133 || 172 || 631 ||
 * East South Central || 15,176 || 8513 || 6663 || 12,049 || 2977 || 95 || 41 || 84 ||
 * West South Central || 26,703 || 19,614 || 7,089 || 20,142 || 3929 || 4539 || 350 || 407 ||
 * Pacific || 39,127 || 35,479 || 3648 || 28,255 || 2454 || 8114 || 453 || 3831 ||
 * Mountain || 13,659 || 9179 || 4480 || 11,762 || 374 || 1992 || 481 || 217 ||
 * Mountain || 13,659 || 9179 || 4480 || 11,762 || 374 || 1992 || 481 || 217 ||

I used a table to answer this question & I also used proportions.

__# Of people that should be chosen from each of the nine geographic regions__
 * New England || 53 delegates || 13207000/248710000= ?/1000 ||
 * Middle Atlantic || 151 delegates || 37602000/248710000= ?/1000 ||
 * East North Central || 168 delegates || 420090000/248710000= ?/1000 ||
 * West North Central || 71 delegates || 17660000/248710000= ?/1000 ||
 * South Atlantic || 175 delegates || 43567000/248710000= ?/1000 ||
 * East South Central || 61 delegates || 15176000/248710000= ?/1000 ||
 * West South Central || 107 delegates || 26703000/248710000= ?/1000 ||
 * Mountain || 54 delegates || 13659000/248710000= ?/1000 ||
 * Pacific || 157 delegates || 39127000/248710000= ?/1000 ||

**B.** **How many of the 1000 delegates should be from metropolitan areas, and how many should be from rural areas?** I solved this problem by using a proportion.

Metropolitan population/US Population = # of delegates from metropolitan areas/# of delegates

This is the same as =

19726000/248710000= ?/1000

To get ? I cross-multiplied 1000 by 192726000. Then I divided the product by 248710000 I got the answer for ?.

19726000 x 1000 = 192726000000 192726000000 divided by 248710000= 775

So 775 delegates should be from the metropolitan area.

To how many delegates should be from the rural area I subtracted the total # of delegates by the delegates that should be from the metropolitan areas.

1000 – 775 = 225.

So 225 people should be from the rural areas.

**C.** **How many of the delegates should be of Hispanic origin?** To solve this problem I used the same method from problem B.

Hispanic population/US population = # of Hispanic delegates/ # of delegates

This is the same as=

22354000/248710000 = ?/1000

To get ? I cross-multiplied 1000 by 22354000. Then I divided the product by 248710000 I got the answer for ?.

22354000 x 1000 = 22354000000

22354000000 divided by 248710000= 90

So 90 delegates should be of Hispanic origin.

**D.** **Four racial groups are named in the data: white; black; Native American-Eskimo-Aleut; & Asian-Pacific Islanders. How many of the total 1000 delegates should represent each of these races? How many should represent the category “all other races” (which is not mentioned in the data)?** I used the same method from Problem C to solve this problem.


 * White || 802 delegates || 199686000/248710000= ?/1000 ||
 * Black || 120 delegates || 29986000/248710000= ?/1000 ||
 * Native American/Eskimo/Aleut || 8 delegates || 1959000/248710000= ?/1000 ||
 * Asian/Pacific Islander || 29 delegates || 7274000/248710000= ?/1000 ||
 * All other races || 41 delegates || 1000 - 959 ||

**E.** **Use your answers to A-D to help you develop a plan for selecting the delegates. Describe your plan in a report that you could submit to the conference organizers.**

I think 53 people should be from New England, 151 people from Middle Atlantic, 168 people from East North Central, 71 people from West North Central, 175 from South Atlantic, 61 from East South Central, 107 people from West South Central, 54 people from Mountain & 157 from Pacific. I believe 775 people of the delegates should be from Metropolitan areas & 225 of the delegates should be from rural areas. Also according to the calculations there should be 802 white delegates, 120 black delegates, 8 Native American/Eskimo/Aleut delegates, 29 Asian/Pacific Islander delegates & 41 delegates from other races.


 * __Follow-Up__**
 * If you could add another criterion to help choose the delegates so that the representation would be fair, what criterion would you add & why?**

I would add immigrants/foreign people because lots of people who live in the U.S are from other countries