Question

Solve the problem below by writing and solving an equation. Be sure to define your variable. There are a total of 122 countries in Africa, Europe, and North America (as of 2012). Europe has twice as many countries as North America, and Africa has seven more than Europe. How many countries are in each of these three continents?

Answer 1

Answer: The number of countries are as follows;

North America = 23, Europe = 46 and Africa = 53

Step-by-step explanation: First of all we identify the variables as algebraic expressions. Hence let North America be N, Europe be E, and Africa be F.

So what we have is;

N + E + F = 122

If Europe has twice as many countries as North America, then Europe can be re-written as 2N. Also if Africa has seven countries more than Europe, then Africa can be re-written as 7 +2N.

Therefore the equation N + E + F = 122 can now be re-written as follows;

N + 2N + 7 + 2N = 122

5N + 7 = 122

Subtract 7 from both sides of the equation

5N = 115

Divide both sides of the equation by 5

N = 23

Hence, North America (N) = 23

Europe (E) = 46

Africa (F) = 53

Answer 2

North America has 23 countries

Europe has 46 countries

Africa ha 53 countries

Explanation:

Firstly to answer the question, we define variables. Let the number of countries in Africa be A, the number of countries in europe be E while the number of countries in North America be N.

Firstly, we are told there are a total number of 122 countries. Mathematically this means the addition of all the countries will give 122

Hence;

N + A + E = 122. •••••••(i)

Secondly we are made to know that Europe has twice as many countries as North America;

Mathematically l, this means

E = 2N. •••••••••(ii)

Thirdly we know that Africa has 7 more countries than Europe;

This mathematically means that

A = E + 7. •••••••••(iii)

Since E = 2N, A = 2N + 7 ••••••••(iv)

Now what to do to find the answer is to substitute equation ii and iv at the same time into equation i

This will give the following;

N + 2N + 2N + 7 = 122

5N = 122 - 7

5N = 115

N = 115/5

N = 23

We recall

E = 2N = 2(23) = 46

Also

A = 2N + 7 = 46 + 7 = 53