SOLUTION: please help me with this problem..thank you! the sum of the digits of a three digit number is 11. If the digits are reversed, the new number is 46 more than five times the old n

Question 130730This question is from textbook ALGEBRA FOR COLLEGE STUDENTS MARK DUGOPOLSKI
: please help me with this problem..thank you!
the sum of the digits of a three digit number is 11. If the digits are reversed, the new number is 46 more than five times the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number? This question is from textbook ALGEBRA FOR COLLEGE STUDENTS MARK DUGOPOLSKI

Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
let u="units digit", t="tens digit", and h="hundreds digit"

"the sum of the digits of a three digit number is 11" __ u+t+h=11

"If the digits are reversed, the new number is 46 more than five times the old number"
__ 100u+10t+h=5(100h+10t+u)+46 __ 100u+10t+h=500h+50t+5u+46

"the hundreds digit plus twice the tens digit is equal to the units digit"
__ h+2t=u

substituting __ (h+2t)+t+h=11 __ 3t+2h=11 __ 3t=11-2h __ multiplying by 50 __ 150t=550-100h

substituting __ 100(h+2t)+10t+h=500h+50t+5(h+2t)+46 __ 101h+210t=505h+60t+46
__ 150t=404h+46

substituting __ 550-100h=404h+46 __ 504=504h __ 1=h

substituting __ 3t+2(1)=11 __ 3t=9 __ t=3

substituting __ 1+3+u=11 __ u=7
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