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Question 1024485: Word problem:-
A three digit number is equal to 17 times the sum of its digits. If 198 is added to the original number,
the digits get interchanged. The addition of the first & the third digit is 1 less than the middle digit.
Find the original number. (steps required)
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617)   (Show Source):
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Word problem:-
A three digit number is equal to 17 times the sum of its digits. If 198 is added to the original number,
the digits get interchanged. The addition of the first & the third digit is 1 less than the middle digit.
Find the original number. (steps required)
Number:  .
Don't you think you need to make an attempt? It's not that difficult to try something!
After your E-Mail, here's the solution:
Let the hundreds, tens, and units digits, be H, T, and U, respectively. From clue 1, we get:
100H + 10T + U = 17(H + T + U)
100H + 10T + U = 17H + 17T + 17U
83H - 7T - 16U = 0 -------- eq (i)
From clue 2, we get:
100H + 10T + U + 198 = 100U + 10T + H
99H - 99U = - 198
99(H – U) = 99(- 2) ------- Dividing by GCF, 99
H – U = - 2 -------- eq (ii)
Finally, clue 3 tells us that:
H + U = T - 1
H - T + U = - 1 ------ eq (iii)
- 7H + 7T - 7U = 7 ---- Multiplying eq (iii) by - 7
83H - 7T - 16U = 0 --- eq (i)
76H - 23U = 7 -------- Adding eqs (iii) & (i) ------- eq (iv)
H – U = - 2 ----- eq (ii)
- 23H + 23U = 46 ----- Multiplying eq (ii) by – 23 ------- eq (v)
76H – 23U = 7 ----- eq (iv)
53H = 53 ------ Adding eqs (v) & (iv)
H, or hundreds digit =  , or 1
1 - U = - 2 -------- Substituting 1 for H in eq (ii)
- U = - 2 - 1
- U = - 3
U, or units digit =  , or 3
1 – T + 3 = - 1 ------- Substituting 1 for H, and 3 for U in eq (iii)
4 – T = - 1
- T = - 1 – 4
- T = - 5
T, or tens digit =  , or 5
Number:
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