Problem 9-15

There are a total of 193 member states (countries) in the United Nations as of 2014. The member states are divided into regional groups. The Asia group has one less member than the Africa group. The European groups are smaller: Eastern Europe has four less than half the Africa group. The Western Europe group (which includes the United States) has 6 more than Eastern Europe. The Latin America group has 21 less than the Africa group. One country (Kiribati, in the central Pacific Ocean) is in no regional group at all.

 How we solved this problem 

1. Firstly, in order to organize ourselves and make our work neater, we determine the given variables we would use in order to create our equations for each different region. Where the Africa group is represented by A, the Asia group is represented by S, the Eastern Europe group is represented by E, the Western Europe group is given by W, Latin America is given by L, and Kiribati is viewable as K. 

2. Once we organized our variables, we then began to analyze the word problem and create separate equations for the 5 regions, knowing that A would be our unknown variable since it is needed to solve the amount of countries in each region. Given this we then followed how the problem stated the regions and formulated these words into formulas. 

• Asia Group: Given the problem, we are given the statement of the Asia having one less member country than the Africa group, therefore since the Africa group is shown by the variable A, we can represent this equation as A-1.
  

• Eastern Europe Group: With the problem, we are informed that the Eastern Europe group has 4 less than half of the Africa group, therefore we know this equation will entail subtraction, multiplication of a number less than one or division. Knowing when something is multiplied by 1/2, we are left with half our total value, we can represent this equation as A(1/2)-4.
  

• Western Europe Group: Due to the fact that Eastern and Western Europe have very similar equations, we simply can use the same format but instead add on to the original equation due to the fact that the problem states that Western Europe has 6 more countries than Eastern Europe leaving us with the equation of A(1/2)-4+6. 
  

• Latin America Group: Once analyzing the problem, we are able to observe that the Latin America group has 21 less countries than the Africa group, entailing subtraction. Therefore the equation can be presented as A-21.
  

1. Once having found the given formulas for each region, as shown above, we then set it to equal 193 since there are 193 countries total in the United Nations. Knowing the given amount of countries in Kiribati, we firstly subtracted 1 from 193 giving us 192. Once we did this we then put all the following formulas we previously created and put them in parentheses and summed them all up. By combining like variables, we have a total of 4 A variables and -24. We then continued to solve by adding 24 to both sides to cancel it out and isolate the A variable, therefore leaving us with 216=4a, and once dividing, leaving A to equal 54.
2. Once having found this main component in our formulas, we then simply plugged in 54 to each of our previously created formulas for each region in order to find their given countries. By doing this we were able to deduce that Africa has 54 countries, Asia has 53, Eastern Europe has 23, Western Europe has 29, Latin America has 33 and Kiribati has 1 country. 

Note: We were then able to confirm these answers since once adding all the totalities (54+53+23+29+33+1), you are left with a total of 193, which was our initial starting point in this problem.