SOLUTION: the sum of the digit's of a three digit number is 14. If the hundred's and unit's are interchanged the resulting number is 594 more than original but if the ten's and the unit's di

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Question 161274: the sum of the digit's of a three digit number is 14. If the hundred's and unit's are interchanged the resulting number is 594 more than original but if the ten's and the unit's digit are interchanged, the now number is more than the original by 36. Find the number?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
"the sum of the digit's of a three digit number is 14" __ h+t+u=14 __ h=14-t-u

"If the hundred's and unit's are interchanged the resulting number is 594 more than original"
__ h+10t+100u=100h+10t+u+594
__ substituting __ 14-t-u+10t+100u=1400-100t-100u+10t+u+594 __ 198u=1980-99t __ 2u=20-t

"ten's and the unit's digit are interchanged, the now number is more than the original by 36"
__ 100h+t+10u=100h+10t+u+36 __ 9u=9t+36 __ u=t+4

substituting __ 2t+8=20-t __ 3t=12 __ t=4

substituting __ u=4+4 __ u=8

substituting __ h=14-4-8 __ h=2

248 is the number