SOLUTION: Kurt is 12 years younger than Mark. When Mark's age is increased by 20% and Kurt's age is increased by 25%, the sum of their ages is 83. Find Kurt's age. I am having a hard time

Question 661570: Kurt is 12 years younger than Mark. When Mark's age is increased by 20% and Kurt's age is increased by 25%, the sum of their ages is 83. Find Kurt's age.
I am having a hard time coming up with the equation to solve. I think the answer is 28, but I need an algebraic equation to solve.
Found 2 solutions by kevwill, lwsshak3:
Answer by kevwill(135) (Show Source): You can put this solution on YOUR website!
Let k = Kurt's age and m = Mark's age. From the first sentence we have
k = m - 12
From the second sentence we have:
m*1.2 + k*1.25 = 83
Substituting the first equation into the second gives:
m*1.2 + (m-12)*1.25 = 83
Expanding:
m*1.2 + m*1.25 - 15 = 83
m*2.45 - 15 = 83
m*2.45 = 98
m = 98 / 2.45 = 40
So Mark is 40 and Kurt is 28.

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Kurt is 12 years younger than Mark. When Mark's age is increased by 20% and Kurt's age is increased by 25%, the sum of their ages is 83. Find Kurt's age.
**
let x=Kurt's age
x+12=Mark's age
25% increase in Kurt's age=25%x=.25x
20% increase in Mark's age=20%(x+12)=.2x+2.4
..
[x+.25x]+[(x+12)+(.2x+2.4)]=83
x+.25x+x+12+.2x+2.4=83
2.45x+14.4=83
2.45x=68.6
x=28
Kurt's age=28
RELATED QUESTIONS
Kurt is 12 years younger than MARK. When Mark's age is increased by 20% and Kurts age is... (answered by josgarithmetic,MathTherapy)
The ratio of Sunita�s age to Mark�s age is currently 3 to 4, and in 12 years, it will be... (answered by josgarithmetic)
Sue is four years older than Mark. Twice Sue�s age plus 5 times Mark�s age is equal to... (answered by richwmiller)
The sum of the ages of mark and Sarah is 102 years. 11 years ago mark was 3 times... (answered by Theo,MathTherapy)
Mark is 6 years older than Stephanie. Two times Mark’s age is 8 less than 4 times... (answered by josgarithmetic)
John's age is 2 years, less than three times Paul his son,s age. His son Mark is 15... (answered by josmiceli,drj)
Pamela is 15 years younger than Jiri. The sum of their ages is 25. What is Jiri’s... (answered by ikleyn)
Ryan�s age increased by 20 is the same age her age times 3. Write an solve equation to... (answered by jorel1380)
1.Determine three consecutive numbers such that the sum of twice the smallest number,... (answered by alanc)