Question

2. The Winter Olympics have been held a total of 21 times on the continents of North America, Europe, and Asia. The number of European sites is 5 more than the total number of sites in North America and Asia. There are 4 more sites in North American than in Asia. (Source: USA Today research) Find the number of Winter Olympic sites on each continent.

Answer 1

Let x represent the number of winter olympics held in North America.

Let y represent the number of winter olympics held in Europe.

Let z represent the number of winter olympics held in North Asia.

The Winter Olympics have been held a total of 21 times on the continents of North America, Europe, and Asia.

This means that

x + y + z = 21

The number of European sites is 5 more than the total number of sites in North America and Asia.

This means that

y = x + z + 5

There are 4 more sites in North American than in Asia.

This means that

x = z + 4

These are the equations. We would solve simultaneously

`\begin{gathered} x\text{ + y + z = 21} \\ y\text{ = x + z + 5} \\ x\text{ = z + 4} \\ \text{Substituting y = x + z + 5 into the first equation, it becomes} \\ x\text{ + x + z + 5 + z = 21} \\ 2x\text{ + 2z + 5 = 21} \\ \text{Substituting x = z + 4 into the above equation, it becomes} \\ 2(z\text{ + 4) + 2z + 5 = 21} \\ 2z\text{ + 8 + 2z + 5 = 21} \\ 4z\text{ + 13 = 21} \\ 4z\text{ = 21 - 13 = 8} \\ z\text{ = }(8)/(4) \\ z\text{ = 2} \\ We\text{ would substitute z = 2 into x = z + 4. It becomes} \\ x\text{ = 2 + 4} \\ x\text{ = 6} \\ We\text{ would substitute x = 6 and z = 2 into x + y + z = 21. It becomes} \\ 6\text{ + y + 2 = 21} \\ 8\text{ + y = 21} \\ y\text{ = 21 - 8} \\ y\text{ = 13} \end{gathered}`

The olympics was held 2 times in North America, 13 times in Europe and 6 times in Asia