Find all two digit numbers each of each of which is 7 times the sum of its digits and write with proper mathematical steps how you found them
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Answer:
Number = 84
Step-by-step explanation:
a two digit number is 7 times the sum of its digits and is also equal to 12 less than three times the product of its digit.
Let say number = xy
Value of number = 10x + y
Sum of digit = x + y
10x + y = 7 ( x + y)
=> 3x = 6y
=> x = 2y
Product of digits = xy
Three times the product of digits = 3xy
10x + y = 3xy - 12
Putting x = 2y
=> 20y + y = 6y² - 12
=> 6y² -21 y - 12 = 0
=> 2y² - 7y - 4 = 0
=> 2y² - 8y + y - 4 = 0
=> 2y(y - 4) + 1(y -4) = 0
=> (2y + 1)(y -4) = 0
=> y = 4
x = 2y = 8
Number = 84
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