how do u solve word prob for 2 digit number, where original number is askd?

Question

A 2 digit nmber is ttaken. Summation of the 2 digit gives 6. And multiplaication of the two digits give 1/3 of the original number. Whhat is the original number?

Answer 1

The 2-digit number can be represented by 10a+b.

a+b=6, ab=⅓(10a+b)=⅓(10a+6-a)=⅓(9a+6)=3a+2.

So, ab=3a+2, b=3+2/a and a+3+2/a=6,

a²+3a+2=6a, a²-3a+2=0=(a-2)(a-1), so a=2 and b=4; or a=1 and b=5.

The number is 15 or 24. The sum of the digits is 6 in each case. 1×5=15/3; 2×4=24/3.