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Question 137004: I would appreciate it if anyone could help me understand how to solve the problem I've typed out and also the solution..thanx!
Question:
A certain number is expressed by three digits whose sum is 10. The sum of the first and last digits is two-thirds(2/3) of the second digit, and if 198 is subtracted from the number, the digits will be reversed. What is the number?
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! let h="hundreds digit", t="tens digit", and u="units digit"
"three digits whose sum is 10" __ h+t+u=10
__ multiplying by 3 __ 3h+3t+3u=30
"sum of the first and last digits is two-thirds(2/3) of the second digit" __ h+u={2/3)t
__ multiplying by 3 __ 3h+3u=2t
substituting __ 3t+2t=30 __ 5t=30 __ t=6
__ substituting __ h+6+u=10 __ h=4-u
"if 198 is subtracted from the number, the digits will be reversed" __ 100h+10t+u-198=100u+10t+h
__ subtracting 10t __ 100h+u-198=100u+h
substituting __ 100(4-u)+u-198=100u+4-u __ 400-100u+u-198=99u+4 __ 198=198u __ 1=u
__ substituting __ h=4-1 __ h=3
361 is the number
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