Question

50 points

a two digit number is obtained by multiplying the sum of the digits be eight. Also, it is obtained by multiplying the difference of the digits by fourteen and adding two. find the number.

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Answer 1

Let the number be    a b,  where a and b are digits.   a ≠ 0.

Given   10 a + b = (a+b) * 8
     =>    2 a = 7 b         ---- (1)

Since 2 and 7 are prime numbers, the only possibilities are :
              a = 7,  b = 2
So the answer could be:  72.

Also given, 
      10 a + b = (a - b) * 14 + 2
              => 15 b = 4 a + 2     ----- (2)
 or,  10 a + b = (b - a) * 14 + 2
            =>  24 a = 13 b + 2    ----- (3)

Putting (1) and (2) together we get:  a = 7 & b = 2.

Putting (1) and (3) together we do not get any integral values.

So the answer is   72.

Answer 2

HEY MATE HERE IS YOUR ANSWER IN ATTACHMENT

$<b>ANSWER = 72</b >$




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