The unit's digit of a 2-digit number is twice the ten's digit. When the number is multiplied by the sum of the digits the result is $$144$$. For another 2-digit number, the ten's digit is twice the unit's digit and the product of the number with the sum of its digits is $$567$$. Then the sum of the two 2-digit numbers is
Solution
For the first number, with tens digit $$t$$ and units digit $$2t$$, the number is $$12t$$ and the digit sum is $$3t$$, so $$36t^2 = 144$$ gives $$t=2$$ and the number is $$24$$. For the second, with units digit $$u$$ and tens digit $$2u$$, the number is $$21u$$ and the digit sum is $$3u$$, so $$63u^2=567$$ gives $$u=3$$ and the number is $$63$$. The sum of the two numbers is $$24+63 = 87$$.
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