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.
Answers
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Step-by-step explanation:
let the original number be10x+y
also 10x+y=7(X+y)
10x+y=7x+7y
10x-7x+y-7y=0
3x-6y=0
x-2y=0--------eq(1)
X=2y------------eq(2)
10x+y=3(xy)-12
10(2y)+y=3(2y×y)-12
20y+y=6y^2-12
6y^2-21y-12=0
6y^2-24y+3y-12=0
6y(y-4)+3(y-4)=0
(y-4)(6y+3)=0
y-4=0 or 6y+3=0
y=4 or y=-3/6
y=4 or y=-1/2
therefore y=4 and X=8
original number is 84
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