SOLUTION: Please help me solve this word problem: The sum of the digits of a two-digit number is 12. The number is 12 times the tens digit. Find the number. I need to know how you got t

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me solve this word problem: The sum of the digits of a two-digit number is 12. The number is 12 times the tens digit. Find the number. I need to know how you got t      Log On


   

Question 257183: Please help me solve this word problem: The sum of the digits of a two-digit number is 12. The number is 12 times the tens digit. Find the number. I need to know how you got the equations please.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let a = the tens digit.
let b = the ones digit.

a + b = 12 (sum of the digits is equal to 12).

10a + b = 12*a (the number is 12 times the tens digit).

solve for a in the first equation to get a = 12-b.

substitute for a in the second equation to get 10*(12-b) + b = 12*(12-b).

simplify to get:

120 - 10b + b = 144 - 12b.

combine like terms to get:

120 - 9b = 144 - 12b.

add 12b to both sides of the equation and subtract 120 from both sides of the equation to get:

3b = 24

divide both sides of the equation by 3 to get:

b = 8

if b = 8, then a = 4 because a + b = 8 + 4 = 12.

the number is 10*a + b = 40 + 8 = 48

48 is equal to 12*a = 12*4 = 48 so that part of the equation is good.

a + b = 4 + 8 = 12 so that part of the equation is also good.

your answer is the number is 48.