SOLUTION: the sum of the digits of a two-digit number is one third of the number. The units digit is 5 more than the tens digit. What is the number?

Question 391887: the sum of the digits of a two-digit number is one third of the number. The units digit is 5 more than the tens digit. What is the number?
Found 2 solutions by stanbon, richard1234:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
the sum of the digits of a two-digit number is one third of the number. The units digit is 5 more than the tens digit. What is the number?
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Let the number be 10t+u
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Equations:
t + u = (1/3)(10t+u)
u = t+5
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Substitute for "u" and solve for "t":
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t + t+5 = (1/3)(10t+t+5)
2t+5 = (1/3)(11t+5)
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6t+15 = 11t+5
5t = 10
t = 2
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u = t+5 = 7
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Ans: The number is 27
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Cheers,
Stan H.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Suppose the number is 10a + b, where a and b are digits. Then,

. To make this an easy, single variable equation we replace all occurrences of b with a+5:

The number is 27.
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