A two - digit number is seven times the sum of its digits and is also equal to 12 less than three times the product of its digits. Find the number.

84

Step-by-step explanation:

Let's say that the two digit number is xy.

Here's what we know:

(x+y) * 7=xy

x*y*3-12=xy

Since this is a multiple of 7, this can be either:

-14

-21

-28

-35

-42

and so on.

Using guess and check, this can be 84.

84

Step-by-step explanation:

let the digit at unit place=x

and at ten's place=y

number = 10y+x

10y+x=7 (x+y)

10y+x=7y+7x

10y-7y=7x-x

3y=6x

y=2x

again

10y+x=3xy-12

10 (2x) + x=3x (2x) - 12

21 x=6x²-12

6x²-21x-12=0

2x²-7x-4=0

2x²-8x+x-4=0

2x (x-4) + 1 (x-4) = 0

(x-4) (2x+1) = 0

x=4, (-1/2, rejected)

y=2*4=8

number=10*8+4=84