Question 8064: A number has two digits whose sum is 8. If 18 is added to the number, its digits are reversed. What is that number.Help me please.
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! if stuck...think of a number example, eg 27. What does this mean?
it means (2x10) + 7.
ok, so our number is xy, which means 10x+y.
Anyway, the first sentence say the sum of the 2 digits is 8, so x+y = 8
if we add 18 to the number, ie 10x+y+18 the result is then yx (ie 10y+x)
--> 10x+y+18 = 10y+x
--> 9x + y + 18 = 10y
--> 9x - 9y + 18 = 0
--> 9x - 9y = -18
--> x - y = -2
So we have 2 equations:
x+y=8
x-y=-2
solve these to give x=3 and y=5 ie we had 35 and 53.
jon.
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