Question 1085222: A number consists of two digits sum of its digit is 15.
if the place of digits are interchange, then the number obtained is 9 less than the original number.
find the original number
Found 3 solutions by josmiceli, addingup, Theo:
Answer by josmiceli(19441)   (Show Source):
Answer by addingup(3677)  (Show Source):
You can put this solution on YOUR website! digit one: x
digit two: y
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x+y = 15 (1)
if interchanged:
10y+x = 10x+y-9
10y+x-10x-y = -9
9y-9x = -9 divide all sides by 9:
y-x = -1 (2)
Add (1) and (2):
x+y = 15
+
-x+y = -1
__________
0+2y = 14
y = 7
the sum of the two digits = 15, so 15-7 = 8
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Check:
sum of the digits: 8+7 = 15
interchanged 9 less: 87-78 = 9 correct
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website!
you are told:
A number consists of two digits sum of its digit is 15.
if the place of digits are interchanged, then the number obtained is 9 less than the original number.
and you are asked:
find the original number
let ab be the original number.
the value of ab is 10 * a + b.
if the original number is ab, then the number with the digits interchanged would be ba.
the value of the number would then be 10 * b + a.
you are told that the sum of the digits is 15 and, if the place of the digits are interchanged, then the number obtained is 9 less than the original number.
this gets you a + b = 15 and 10b + a = 10a + b - 9
you have 2 equations that need to be solved simultaneously.
they are:
a + b = 15
10b + a = 10a + b - 9
in the first equation, solve for b to get b = 15 - a
in the second equation, replace b with 15 - a to get:
10 * (15 - a) + a = 10a + (15 - a) - 9
simplify to get:
150 - 10a + a = 10a + 15 - a - 9
combine like terms to get:
150 - 9a = 9a + 6
subtract 6 from both sides of the equation and add 9a to both sides of the equation to get 144 = 18a.
divide both sides of the equation by 18 to get 144/18 = a
solve for a to get a = 144/18 = 8
since a + b = 15, then b must be equal to 7.
the original number is ab which is 87.
the new number is ba which is equal to 78 which is equal to 9 less than 87.
the sum of the digits is 15.
all the requirements of the problem have been satisfied, so the solution looks good.
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