SOLUTION: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then th

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then th      Log On


   

Question 1101895: In a two-digit number, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is
Found 3 solutions by ikleyn, richwmiller, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
24.

Solved MENTALLY in 4 seconds.


Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
It is an absolute REQUIREMENT that you MUST SHOW ALL WORK. Showing work is the best way to demonstrate your competence. Solutions without sufficient work shown are worthless.
Telling us that you solved mentally tells us nothing since we cannot read your mind.
You could mention your thought process.
What did you do mentally?
What did you consider?
Did you just grab the answer out of the air?

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
t, the Tens digit
u, the Units digit
10t%2Bu, the two-digit number


The description literally translated into a system of equations:
system%28u-t=2%2C%2810t%2Bu%29%28t%2Bu%29=144%29
Solve this system.


Use u=t+2 to substitute into the Product_144 equation and simplify:
.
%2811t%2B2%29%282t%2B2%29=144
.
11t%5E2%2B13t-70=0

Discriminant, 169%2B4%2A11%2A70=3249=57%5E2;


t=%28-13%2B57%29%2F%282%2A11%29------using general solution for quadratic equation


highlight%28t=2%29
-
highlight%28u=4%29

The two-digit number is: highlight%2824%29.