Problem solving

Question

The sum of the digits of a two-digit number is 13. Twice the ones digit is two more than four times the tens digit. Find the number.

 

Answer 1

Let x be the tens digit and y be the ones digit. First, x + y = 13. Next, twice the ones digit is 2y, and four times the tens digit is 4x. 2y is two more than 4x, so 2y = 4x + 2. Now we have a two equation system. Solve one variable interms of the other and substitute. x + y = 13, so y = 13 - x. Put this into the second equation to get rid of y. 2(13 - x) = 4x + 2. Simplify, 26 - 2x = 4x + 2. Isolate the x's and the constants by adding 2x to both sides, and subtracting 2 from both sides giving 24 = 6x. Divide by 6 to solve for x, and x = 4. Now plug 4 in for x in the first equation and y = 4 = 13, so y = 9. Hope that helps.