The area of the Sahara desert is 7 times the area of the Gobi desert. If the sum of their areas is 4,000,000 square miles, find the area of each desert

Question

1. Answer question
2. show work 
3. solution

Answer 1

Begin by expressing the problem in terms of simple algebraic equations. We want to know the area of the Sahara (S) and the Gobi (G) deserts. The problem tells us that the area of these two deserts combined is 4,000,000. Thus:

 

S + G = 4,000,000

 

The other bit of information the problem gives us is that the Sahara is 7 times the area of the Gobi desert. Thus:

 

S = 7*G

 

Now, we can substitute 7*G for S in the first equation:

 

7*G + G = 4,000,000

 

Which simplifies to:

 

8G = 4,000,000

 

And dividing both sides by 8 solves for G:

 

G = 4,000,000/8 = 500,000

 

Now that we know the area of the Gobi is G = 500,000, since the Sahara S is 7 times this size, we have:

 

S = 7*G = 7*500,000 = 3,500,000

 

So our final answer is: the Sahara is 3,500,000 square miles, and the Gobi is 500,000 square miles. To check our work, we can double check that the criteria in the problem are both satisfied:

 

1) The Sahara is 7 times larger than Gobi, CHECK

2) The Sahara and Gobi combined are 4,000,000 square miles, CHECK

Answer 2

What we know from the problem:

 

Sahara desert is 7 times the area of the Gobi desert.

 

S = 7G

 

The sum of their areas is 4,000,000 square miles.

 

S + G = 4,000,000 mi²

 

find the area of each desert.

 

Substitute S = 7G in the above equation and solve.

 

7G + G = 4,000,000 mi²

 

Then substitute this in for the area of the Gobi, G and solve for S.