Math Problem?
2017-06-11 6:37 am
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 to the sum of the other two. Find the number.
回答 (5)
2017-06-11 6:42 am
This is more a logic puzzle than a math puzzle. If three digits equal 6, and they're all different, they have to be 1, 2 and 3. There's no other combination of 3 different digits that equals six.
So if the hundreds digit is twice the units digit, that can only mean the hundreds digit is 2 and the units digit is 1. Meaning the tens digit must be 3.
So if the hundreds digit is twice the units digit, that can only mean the hundreds digit is 2 and the units digit is 1. Meaning the tens digit must be 3.
2017-06-11 6:50 am
x+y+z = 6 ................ [1]
x = 2z ...................... [2]
y = x+z .................... [3]
[2]→[3]:
y = 2z + z
y = 3z ...................... [4]
[2], [4] → [1]:
x+y+z = 6
2z + 3z + z = 6
6z = 6
z = 1
[4]:
y = 3z
y = 3(1)
y = 3
[2]:
x = 2z
x = 2(1)
x = 2
Therefore, the number is 231.
x = 2z ...................... [2]
y = x+z .................... [3]
[2]→[3]:
y = 2z + z
y = 3z ...................... [4]
[2], [4] → [1]:
x+y+z = 6
2z + 3z + z = 6
6z = 6
z = 1
[4]:
y = 3z
y = 3(1)
y = 3
[2]:
x = 2z
x = 2(1)
x = 2
Therefore, the number is 231.
2017-06-11 6:57 am
Just try testing numbers as this is quite basic:
a + b + c = 6
if a = 1
c = 0.5
b = 1.5
This cannot be right!
if a = 2
c = 1
b = 3
2 + 3 + 1 = 6
a + b + c = 6
if a = 1
c = 0.5
b = 1.5
This cannot be right!
if a = 2
c = 1
b = 3
2 + 3 + 1 = 6
2017-06-11 6:45 am
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 to the sum of the other two.
x + y + z = 6
x = 2z
y = x + z
x = 2, y = 3, z = 1
The number is 231.
The hundreds digit is twice the units digit,
and the tens digit equals to the sum of the other two.
x + y + z = 6
x = 2z
y = x + z
x = 2, y = 3, z = 1
The number is 231.
2017-06-11 9:00 pm
a + b + c = 6
a = 2c
b = a + c
b = 3c
a + b + c = 6 => 2c + 3c + c = 6
=> c = 1, a = 2, b = 3
the 3 digit number is 231
a = 2c
b = a + c
b = 3c
a + b + c = 6 => 2c + 3c + c = 6
=> c = 1, a = 2, b = 3
the 3 digit number is 231
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