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.Com
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) (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.
RELATED QUESTIONS
Please,.,.help me solve this problem,,
The sum of the digits of a two-digit number is... (answered by drj)
I need your help with this digit problem: The sum of the digits of a two-digit number is... (answered by Theo)
the sum of the digits of a two digit number is 12. the number is 13 times the tens digit. (answered by Abbey)
Please help me out with this maths.
The sum of the digits of a two-digit number is 12.... (answered by rothauserc)
A certain two digit number has a value that is three times the sum of it's digits. The... (answered by ankor@dixie-net.com)
The sum of the digits of a three-digit number is 12. The tens digit is two times the... (answered by mananth)
A certain two digit number has a value that is eight less than five times the sum of it's (answered by lwsshak3,mathstutor458)
Please help me solve this word problem leading to quadractic
The sum of the digits of a... (answered by ankor@dixie-net.com)
The sum of the digits of a two digit number is 12. The tens digit is three times the... (answered by checkley71)