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?

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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:

$36$