Question

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

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Answer 1

Answer:

84

Step-by-step explanation:

ab- is the 2-digit number (ab is 10a+b)

1. 10a+b= 7(a+b) => 3a=6b => a=2b
2. 10a+b= 3ab-12 =>

• 10*2b+b=3*2b*b-12
• 6b²-21b-12=0

• 2b²-7b-4=0
• solving we get b=4
• then a=2b=2*4=8

Given number is 84

Proof:

• 7*(8+4)=7*12=84
• 3*8*4-12=96-12=84

Answer 2

Answer:

84

Step-by-step explanation:

LET THE TWO DIGIT NO. BE

x  y . WITH x BEING IN THE TENTH'S PLACE AND y IN THE ONE'S PLACE.

THEREFORE THE VALUE OF THE NO. IS 10x+y.

NOW, 10x+y = 7(x+y)

10x+y = 7x+7y  ,  3x=6y  , x=2y

AND ALSO, 10x+y = 3xy-12

AS x=2y   ,  10*2y+y = 3*2y*y-12

21y = 6y^2-12  ,  6y^2-21y-12=0

6y^2-24y+3y-12=0  ,  6y(y-4)+3(y-4)=0

6y+3=0  or y-4=0

y=-3/6 ,rejected cause a digit cannot be a fraction.  THEREFORE, y=4

x=2*4=8

HENCE , THE NO. IS 10x + y = 80 + 4 = 84