Question

A two digit number is 7 times the sum of its digits and is equal to 12 less than three times the product of its digits. Find the number.

Answer 1

Dear Student,

$$\begin{gathered} Letthetwodigitnumberbe10x+y \\ Then,10x+y=7\left(x+y\right) \\ 10x+y=7x+7y \\ 3x=6y \\ x=2y \\ Also,10x+y=3\left(xy\right)-12 \\ 10x+y=3xy-12 \\ Substitutex=2y,weget \\ 20y+y=6y^2-12 \\ 6y^2-21y-12=0 \\ 6y^2-24y+3y-12=0 \\ 6y\left(y-4\right)+3\left(y-4\right)=0 \\ \left(y-4\right)\left(6y+3\right)=0 \\ y=4 \\ x=2y;x=8 \\ Hence,thenumberis84 \end{gathered}$$
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