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Question 519069: One of the digits of a two digit number is 6, whose sum is half of their
product, and whose product is half of the reverse order number. What is
the number?
Found 2 solutions by Edwin McCravy, mamiya:
Answer by Edwin McCravy(20060)   (Show Source):
You can put this solution on YOUR website! One of the digits of a two digit number is 6, whose sum is half of their
product, and whose product is half of the reverse order number. What is
the number?
Let t = the tens digit
Let u = the ones or units digit.
One of the digits of a two digit number is 6.
We aren't told which it is so we have to try both possibilities.
Case 1: u = 6
whose sum is half of their product
t + 6 =  ·6t
t + 6 = 3t
6 = 2t
3 = t
So the number is 36
and whose product is half of the reverse order number
The product is 3*6 = 18 but 18 is not half of the reverse 63.
So Case 1 is eliminated, so it's not 36.
Case 2: t = 6
whose sum is half of their product
6 + u = ·6u
12 + 2u = 6u
12 = 4u
3 = u
So the number is 63
and whose product of the half of the reverse order number
The product is 6*3 = 18 and 18 is indeed half of the reverse 36.
So that's it. The number is 63.
Edwin
Answer by mamiya(56)  (Show Source):
You can put this solution on YOUR website!
let xy be the number, where x is the first digit and y the second one.
based on the question, x+y=x*y/2 and x*y=yx/2 ( yx represents a number not a product)
so we have, x+y=x*y/2
x*y= (10y+x)/2
2(x + y)= x*y
x*y= (10y+x)/2
so, 2(x+y)=(10y+x)/2
2*2(x+y)=2(10y+x)/2
4(x+y)=10y+x
3x=6y
x=2y
we know that x and y are integer numbers because they are digits of a number.
the question says, one of the digit is 6 but we let's say y is the one who is 6
if y=6, we would have, x=2*6=12, and this would make any sense since x is supposed to be a digit not a number, so y is not 6. since y is not 6, we can affirm the digit that is 6 is x.
so x=6 , y=x/2=6/2=3.
so xy=63.
the answer is 63.
we can check our answer.
6+3=(6*3)/2 and 6*3=36/2
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