A two digit number is 4 times the sum of its digits and twice the product of its digit.FIND THE NUMBER

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asked Jun 26, 2015 175k views

5 votes

A two digit number is 4 times the sum of its digits and twice the product of its digit.FIND THE NUMBER

Mathematics
high-school

Vasily A asked

by Vasily A

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1 Answer

5 votes

x - tenths digit
y - units digit

$10x+y=4(x+y)\\ 10x+y=2xy\\\\ 10x+y=4x+4y\\ 10x+y=2xy\\\\ 6x=3y\\ 10x+y=2xy\\\\ 3x=y\\ 10x+y=2xy\\\\ 10x+3x=2x\cdot3x\\ 13x=6x^2\\ 6x^2-12x=0\\ 6x(x-2)=0\\ x=0 \vee x=2\\\\ y=3\cdot2\\ y=6\\\\ 10\cdot2+6=\boxed{26}$

Thenickdude answered Jul 2, 2015

by Thenickdude

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