algebra word problem

Question

The units' digit of a two-digit numeral is 5 more than the tens' digit. The number is 3 times the sum of its digits. Find the numeral.

Answer 1

Let x be the 10's digit.  Since it's the tens digit, its value is 10x

• The units digit is 5 more than the tens digit = x+5
• The number is 3 times the sum of its digits

 

      10x + (x+5) = 3(x + x+5)

      11x + 5 = 6x + 15

      5x = 10

      x = 2

 

The number is 10x + x+5 = 10*2 + 2+5 = 20 + 7 = 27

 

Check:

      The number is 3 times the sum of its digits

      27 = 3*(2+7)

      27 = 3*9

      27 = 27

      Check!