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Question 811623: In a three digit number, the sum of its ones digit and tens digit is ten. Its tens digit is twice its hundreds digit, and its hundreds digit is twice its ones digit. What is the number?
Answer by Edwin McCravy(20055)   (Show Source):
You can put this solution on YOUR website!
Two ways. The easy way and the algebra way.
Its tens digit is twice its hundreds digit, and its hundreds digit is twice its ones digit.
That tells us it's either 241 or 482.
the sum of its ones digit and tens digit is ten
That rules out 241, so it's 482.
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Harder algebra way:
In a three digit number,
Let h = the hundreds digit.
Let t = the tens digit.
Let u = the ones or UNITS digit.
the sum of its ones digit and tens digit is ten.
(1) u+t=10
Its tens digit is twice its hundreds digit,
(2) t=2h
and its hundreds digit is twice its ones digit.
(3) h=2u
Use (3) to substitute 2u for h in (2)
t=2(2u)
(4) t=4u
Use (4) to substitute 4u for t in (1)
u+(4u)=10
5u=10
(5) u=2
Use (5) to substitute 2 for u in (4)
t=4(2)
(6) t=8
Use (6) to substitute 8 for t in (3)
h=2(2)
h=4
h=4, t=8, u=2,
Answer: 482
Checking:
In a three digit number, the sum of its ones digit, 2, and tens digit, 8, is ten. That checks.
Its tens digit, 8, is twice its hundreds digit, 4. That checks.
and its hundreds digit, 4, is twice its ones digit, 2. That checks.
Edwin
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