The units digit of the two digit integer is 3 more than the tens digit. The ratio of the product of the digits to the integer is 1/2. How do you find this integer?

Question

2311 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-14T17:54:17

#36#

Suppose the tens digit is #t#.

Then the units digit is #t+3#

The product of the digits is #t(t+3) = t^2+3t#

The integer itself is #10t+(t+3) = 11t+3#

From what we are told:

#t^2+3t = 1/2(11t + 3)#

So:

#2t^2+6t = 11t + 3#

So:

#0 = 2t^2-5t-3 = (t-3)(2t+1)#

That is:

#t = 3" "# or #" "t = -1/2#

Since #t# is supposed to be a positive integer less than #10#, the only valid solution has #t=3#.

Then the integer itself is:

#36#