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.
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-> 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.
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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.
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.
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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
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