Question

The three countries of greatest area in the world are the Soviet Union, Canada, and China, with a combined area of 41,939,000 km squared. The area of Canada is 415,000 Km squared greater than that of China, while the combined area of Canada and China is 2,865,000 Km squared less than that of the soviet union. What is the area of each country.

Answer 1

Soviet union: area = 22,402,000 km^2.

Canada : area = 9,976,000 km^2

China: area = 9,561,000 km^2.

Explanation:

Let area of Canada be d, area of China be c and area of the Soviet union be s.

c + d + s = 41,939,000

d = c + 415,000

s = c + d + 2,865,000 Rearranging this equation:

s - c - d = 2865000 Adding this equation to the first equation:

2s = 44,804,000

s = 22,402,000

Substituting for s in the third equation:

22,402,000 = c + d + 2,865,000

c + d = 22,402,000 - 2,865,000

c + d = 19,537.000 Rearranging the second equation we get:

-c + d = 415,000 Adding the last 2 equations:

2d = 19,952,000

d = 9,976,000.

Substituting in the first equation:

c + 9,976,000 + 22,402,000 = 41,939,000

= 41,939,000 - 9,976,000 - 22,402,000

c = 9,561,000.

Answer 2

Explanation:

Lets give each country a variable

Let the Soviet Union be x, Canada be y, and China be z.

We know their combined area is 41,939,000, so we can create the equation

x + y + z = 41,939,000

Then we know that the area of Canada is 415,000 greater than China, so we create the equation

z + 415,000 = y

Then using the last bit of info, the combined are of China and Canada is 2,865,000 less than the Soviet Union, we can for this equation

y + z + 2,865,000 = x

Know we must use system of equations to solve for x, y, and z.

If you look at the last and the first equation that we created, you can see that we can substitute x from the last to the first

x = y + z + 2,865,000, and we will put this into x + y + z = 41,939,000 to get

y + z + 2,865,000 + y + z = 41,939,000

We still need to get rid of the variable y or z so we can solve for one of them. This is where we use the second equation.

From our second equation we know that z + 415,000 = y, and we can put this into the new equation we just created, y + z + 2,865,000 + y + z = 41,939,000 to get

z + 415,000 + z + 2,865,000 + z + 415,000 + z = 41,939,000

Then we can simplify by adding like terms, and that will get us

4z + 3,695,000 = 41,939,000

Subtract 3,695,000 from both sides to get

4z = 38,244,000

Divide by 4 on both sides and get

z = 9,561,000

We can substitute this value into our original second equation z + 415,000 = y to find the value of y, and that would be

9,561,000 + 415,000 = y

y = 9,976,000

Then we can plug the values of y and z into our third original equation, y + z + 2,865,000 = x to find the value of x.

9,976,000 + 9,561,000 + 2,865,000 = x

Then doing the addition, you get x = 22,402,000

So the area of Canada is 9,976,000 km^2, China is 9,561,000 km^2, and the area of the Soviet Union is 22,402,000 km^2