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Question 1133718: A number consist of 3 digits whose sum is 14, the middle digit is equal to the number of the other two. If you reverse its digit the original number will be lesser by 99. Find the number.
Found 3 solutions by josgarithmetic, ankor@dixie-net.com, greenestamps:
Answer by josgarithmetic(39617)   (Show Source):
Answer by ankor@dixie-net.com(22740)  (Show Source):
You can put this solution on YOUR website! A number consist of 3 digits whose sum is 14,
a + b + c = 14
the middle digit is equal to the sum of the other two.
b = a + c
If you reverse its digit the original number will be lesser by 99.
100a + 10b + c + 99 = 100c + 10b + a
100a - a + 10b - 10b + 99 = 100c - c
99a + 99 = 99c
simplify, divide by 99
a + 1 = c
:
We got 3 simple equation and 3 unknowns so this should be easy
in the 2nd equation, replace c with a+1
b = a + (a+1)
b = 2a + 1
:
in the first equation replace b with (2a+1); replace c with (a+1)
a + (2a+1) + (a+1) = 14
4a + 2 = 14
4a = 14 - 2
4a = 12
a = 3
then
b = 2(3) + 1
b = 7
and
c = 3 + 1
c = 4
:
Check 3 + 7 + 4 = 14 and 374 + 99 = 473
Find the number. 374
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Take any 3-digit number, reverse the digits, and find the difference between the two numbers. The difference will always be 99n, where n is the difference between the first and last digits.
In this problem, the middle digit is the sum of the other two digits, and the sum of all three digits is 14. That means the middle digit is 7.
Since the difference between the two 3-digit numbers is 99, the difference between the first and last digits is 1. Then, since the sum of the first and last digits is 7, those digits are 3 and 4. So the two 3-digit numbers are 374 and 473.
The problem says that the original number is smaller, so...
ANSWER: the original number is 374
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