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## solving Word Problems

By air, the distance from Melbourne, Australia, to Cairo, Egypt, is 2338 miles more than the distance from Madrid, Spain, to Bangkok, Thailand.  If the total of these distances is 15,012 miles, find the distance from Madrid to Bangkok.

let x=distance from Madrid to Bangkok
therefore the distance from Melbourne to Cairo is x+2338 (this distance is 2338 miles more than the distance x from Madrid to Bangkok)
the total of these distances is 15,012 miles
x+(x+2338)=15,012
2x+2338=15,012
2x=12,674
x=6,337 miles

Hi Dawn;
I hope you understand that
Melbourne is in Australia
Cairo is in Egypt
and
Bangkok is in Thailand.

(total distance)-(Melbourne to Cairo=(Madrid to Bangkok)
15,012-2,338=12,674

Let's check our work...
(Melbourne to Cairo)+(Madrid to Bangkok) ?? (total distance)
2,338+12,674 ?? 15,012
15,012=15,012

I did not realize it is a one-way trip.
Australia to Egypt call it A
Spain to Thailand call it S
first sentence can be written algebraically as A=2338+S
the total distance is A+S=15012. We need to find S so substituting in for A
2338+S+S=15012
2338+2S=15012. Subtracting from both sides and solving.
-2338       -2338
2S=12674. DivIDE by 2
S=6337 miles

•-------- → ------•
x  miles

Melbourne                Cairo
•----------- → --------•
(x + 2338) miles

x + (x + 2338) = 15012

2x + 2338 = 15012

2x = 15012 − 2338

2x = 12674

x = 12674 ÷ 2

x = 6337 miles   distance from Madrid to Bangkok

~~~~~~~~~
6337 + (6337 + 2338) = 15012
6337 +        8675       = 15012
15012                = 15012