A two digit number is such that the product of its digits is 35. If 18 is added to the number, the digits interchange the places. Find the number. Solve using system of equations in two variables.

Question

dumbcow · Answer

easy :P

anonymous · Answer

how

dumbcow · Answer

@FoolForMath will show you

anonymous · Answer

Lets say the number is $ 10x+y$

$$x\times y = 35 \tag{1} $$
$$ 10x+y +18 = 10y+x \implies  18 + 9 x - 9 y =0 \tag{2} $$

anonymous · Answer

ok

anonymous · Answer

I too got the same equation, but you will end up with a quadratic equation. I tried solving it, but I got a fractional answer.

anonymous · Answer

y=7 and x =5 .. the number is 57

anonymous · Answer

Can you show me how you got it?

callisto · Answer

ab = 35
10a+b+18 = 10b+a
10a +(35/a) +18 = 10(35/a) +a
9a^2 + 18a -315 =0
a=5 or a=-7 (rejected)
b=35/5 = 7
=> number is 57

anonymous · Answer

You got a = 5 by solving the quadratic equation?

anonymous · Answer

I must have made a mistake somewhere, thanks anyway.

anonymous · Answer

Who do I give the medal to? Fool or Callisto?

callisto · Answer

Fool :)

anonymous · Answer

Callisto!

anonymous · Answer

OK, Fool can give to Callisto, I'll give to Fool.

dumbcow · Answer

ok here is easy way...no need for equations
what are the factors of 35.....5 and 7
so its either 57 or 75
75-57 = 18

answer = 57

callisto · Answer

using system of equations :P

anonymous · Answer

@dumbcow: There is another easy way, just go through the options ;)

dumbcow · Answer

well yeah if its multiple choice...but thats no fun

callisto · Answer

The easiest way is that the answer pops out immediately :)

anonymous · Answer

You're right callisto but this is a subjective question.