Consider a two digit number, where the sum of the digits is 9. If the number is twice the product of it's two digits, find the number?

Question

Well... I am high school student, and urgently need as answer to this question, I really am new to this site and don't really know what to type in the description of a question I ask. That's my other question, why do we need to describe the question?

Answer 1

using algebra...

ab is the number which means...

10a+b

a+b=9

10a+b=2ab

a=9-b from a+b=9

substitute

10(9-b)+b=2(9-b)b

90-10b+b=18b-2b²

90-9b=18b-2b²

2b²-18b+90-9b=0

2b²-27b+90=0

2*90=2*3*3*2*5=(2*3*2)*(3*5)=12*15 and 12+15=27

factor

(2b    )(b    )=0

(2b  15)(b  6)=0

(2b-15)(b-6)=0

using only (b-6)

b-6=0

b=6

a+b=9

a+6=9

a=3

the number is 36

 

Answer 2

x + y = 9

2xy = N

 

We can solve through trial and error since there are only a few combos of 2 numbers that sum to 9.

 

0,9

1,8

2,7

3,6

4,5

 

2(0)(9) = 09

0 = 9

 

2(1)(8) = 18

16=18

 

2(2)(7) = 27

28 = 27

 

2(3)(6) = 36

36 = 36

 

2(4)(5) = 45

40 = 45

 

So we can see that the answer has to be 36.