SOLUTION: The total length of the coastlines of Canada, the United States, and Mexico is about 270 000 km. The Canadian coastline is 16 times the average length of the coastlines of the U.S.

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The total length of the coastlines of Canada, the United States, and Mexico is about 270 000 km. The Canadian coastline is 16 times the average length of the coastlines of the U.S.      Log On


   

Question 1203278: The total length of the coastlines of Canada, the United States, and Mexico is about 270 000 km. The Canadian coastline is 16 times the average length of the coastlines of the U.S. and Mexico. The U.S. coastline is 10 000 km longer than the Mexican coastline. Find the length of the coastline of each country, in kilometres.
Found 3 solutions by ikleyn, josgarithmetic, greenestamps:
Answer by ikleyn(52788) About Me  (Show Source):
You can put this solution on YOUR website!
.
The total length of the coastlines of Canada, the United States, and Mexico is about 270 000 km.
The Canadian coastline is 16 times the average length of the coastlines of the U.S. and Mexico.
The U.S. coastline is 10 000 km longer than the Mexican coastline.
Find the length of the coastline of each country, in kilometres.
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        When I read this post, honestly, I do not understand, what these words precisely mean 

        The Canadian coastline is 16 times the average length of the coastlines of the U.S. and Mexico.

        They may mean Canadian = 16%2A%28%28US%2BMexican%29%2F2%29

        or they may mean Canadian = 16*(US+Mexican).

        Of these two possible interpretations, I used second one. 


x = that of the Mexican coastline

(x+10000) = that of the US coastline

16(x+(x+10000)) = that of the Canada coastline


Total equation

    x + (x+10000) + 16(x+(x+10000)) = 270000 kilometers.


Simplify and find x

    34x = 270000 - 10000 - 160000 = 100000

      x = 100000/34 = 2941.2 km  for the Mexican coastline.


Next calculate (2941.2+10000) for the US coastline and  16(2941.2 + (2941.2+10000)) for the Canada coastline.

That's all.


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To say "16 times the average length of the coastlines of the U.S. and Mexico"
it is very curved way to express simple statement

        "8 times the length of the coastlines of the U.S. and Mexico".

No one professional Math writer would write it as it is made in the post,
since otherwise all the people around will laugh on it.




Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
REGION                  COASTLINE LENGTH, km
Canada                  16(1/2)(m+m+10000)
Mex.                     m
US                       m+10000
TOTAL                    270000

Solve this and evaluate the other two lengths: 8%282m%2B10000%29%2Bm%2B%28m%2B10000%29=270000

---

16m%2B8%2A10000%2B2m%2B10000=270000
18m=270000-80000-10000
18m=270000-90000
18m=180000
highlight%28m=10000%29
.
.


recheck
can. 8(2*10000+10000)=8(30000)=240000
mex. 10000
us 20000
sum: 270000

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


For the moment, let x represent the average length of the American and Mexican coastlines. Then the total of 270,000 km is composed of

Mexico: x
US: x
Canada: 16x

So the length of the Canadian coastline is 16/18 = 8/9 of the total, which is 8*30,000 = 240,000.

That leaves 30,000 km for the combined length of the US and Mexican coastlines.

Now use the fact that the US coastline is 10,000 km longer than the Mexican coastline. Simple mental arithmetic shows that the Mexican coastline is 10,000 km and the US coastline is 20,000 km.

Or if you want formal algebra for this part of the problem....

x = Mexican coastline
x+10000 = US coastline
x+x+10000 = 30000
2x+10000 = 30000
2x = 20000
x = 10000
Mexico: x = 10000
US: x+10000 = 20000

ANSWERS:
Mexico: 10,000 km
US: 20,000 km
Canada: 240,000 km