SOLUTION: karen is twice as old as marie.four years from now,the sum of their ages will be 44.how old is karen?

Question 205069: karen is twice as old as marie.four years from now,the sum of their ages will be 44.how old is karen?
Found 2 solutions by edjones, Edwin McCravy:
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let k=karen's age now & m=marie's age.
k=2m
k+4+m+4=44
2m+4+m+4=44 substitute 2m for k
3m+8=44
3m=36
m=12
k=24
.
Ed
Answer by Edwin McCravy(20059) (Show Source): You can put this solution on YOUR website!
Edwin's solution:
Karen is twice as old as marie. Four years from now, the sum of their ages will be 44. How old is Karen?

Make this chart: age age now then KAREN | ------------------- MARIE | ------------------ You can do it with either one unknown or two unknowns. With one unknown: We must define one of their ages in terms of the other. Then the "other" will be the one we will represent by an unknown (letter). Since the sentence

"Karen is twice as old as Marie"

defines Karen's age in terms of Marie's age, we choose Marie's age to be the unknown, M. We will define Karen's age in terms of M, Marie's age, Karen's age now = 2 times Marie's age M now, so Karen's age now = 2M We fill in the chart with M for Marie's age now and 2M for Karen's age now age age now then KAREN 2M | ------------------- MARIE M | ------------------- Then we read

"four years from now,..."

So we add +4 to each of their ages to get their ages then: age age now then KAREN 2M | 2M+4 ------------------- MARIE M | M+4 ------------------ Then we read:

"...the sum of their ages will be 44."

So we add (2M+4) plus (M+4) and set that equal to 44: (2M+4)+(M+4)=44 2M+4+M+4=44 3M+8=44 -8 -8 ------- 3M =36 M=12 So Marie is 12. Then Karen's age is 2M or 2(12) or 24. Checking: Four years fom now they will be 16 and 28, and those have sum 44. it checks. ======================= With two unknowns: age age now then KAREN K | K+4 ------------------- MARIE M | M+4 ------------------ Simplify and solve that system of equations and you'll get K=24 and M=12 Edwin

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