SOLUTION: The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit, and the tens digit equals the sum of the other two. Find the number.

Question 1201474: The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit,
and the tens digit equals the sum of the other two. Find the number.
Found 4 solutions by mananth, MathTherapy, greenestamps, josgarithmetic:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit,
and the tens digit equals the sum of the other two. Find the number.
Let the digits be x , y ,z
x hundred's place
y ten's place
z unit's place
The number will be xyz
The sum of the digits of a three-digit number is 6
x+y+z=6
The hundreds digit is twice the units digit,
x = 2z
the tens digit equals the sum of the other two
y=x+Z
x+y+z=6 ( substitute y)
x+x+z+z =6
2x+2z=6
But x =2z ( substitute x=2z)
2(2z)+2z=6
6z=6
z=1
x=2z
x= 2*1 =2

Y=x+z
y = 1+2 =3
The number is 231

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

The sum of the digits of a three-digit number is 6. The hundreds digit is twice the units digit, and the tens digit equals the sum of the other two. Find the number. Let units digit be U Then hundreds digit = 2U Since the tens digit is equal to the sum of the other 2, the tens digit is U + 2U = 3U Since ALL digits sum to 6, we get: 2U + 3U + U = 6 6U = 6 Units digit, or Hundreds digit: 2U = 2(1) = 2 Tens digit: 3U = 3(1) = 3 Number: 231

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Presumably a formal algebraic solution was wanted; a couple of other tutors have shown such solutions.

But simple logical reasoning (good brain exercise!!) solves the problem in very little time.

The sum of the digits is 6, and the tens digit is equal to the sum of the other two digits. That means the tens digit is half the sum of all three digits, so the tens digit is 3.

That leaves the sum of the units and hundreds digit being 3; and since the hundreds digit is twice the units digit, the units digit is 1 and the hundreds digit is 2.

ANSWER: 231

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Three digit number,

Sum of digits is 6.

The hundreds digit is twice the units digit,
and the tens digit equals the sum of the other two.

As a system of equations

----------equation in one single variable

------use this to find the other two digits.
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