SOLUTION: A number between 300 and 400 is 40 times the sum of its digits. The tens digit is six more then the units digit. Find the number.
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Question 699470: A number between 300 and 400 is 40 times the sum of its digits. The tens digit is six more then the units digit. Find the number. Found 2 solutions by stanbon, MathTherapy:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A number between 300 and 400 is 40 times the sum of its digits. The tens digit is six more then the units digit. Find the number.
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3*10^2 + b*10 + c = 40(3+b+c)
b = c + 6
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Substitute for "b" and solve for "c":
300 + 10(c+6) + c = 40(3+c+6+c)
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300 + 10c + 60 + c = 40(9+2c)
360 + 11c = 360+80c
11c = 80
c = 80/11
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Comment: c should be a whole number.
Please check the posting of the problem.
Cheers,
Stan H.
You can put this solution on YOUR website!
A number between 300 and 400 is 40 times the sum of its digits. The tens digit is six more then the units digit. Find the number.
Since number is between 300 and 400, then the hundreds digit MUST be 3
Let the tens, and units digits be T, and U, respectively
Then: 300 + 10T + U = 40(3 + T + U)
300 + 10T + U = 120 + 40T + 40U
10T – 40T + U – 40U = 120 – 300
- 30T – 39U = - 180
- 3(10T + 13U) = - 3(60)
10T + 13U = 60 ------ eq (i)
T = U + 6 ------ eq (ii)
10(U + 6) + 13U = 60 --------- Substituting U + 6 for T in eq (i)
10U + 60 + 13U = 60
23U = 0
U, or units digit = 0
T = 0 + 6 ------ Substituting 0 for U in eq (ii)
T, or tens digit = 6
Three-digit number between 300 and 400 =
You can do the check!!
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