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October 3rd, 2007, 10:49 PM  #1 
Newbie Joined: Sep 2007 Posts: 4 Thanks: 0  word problem
At present sum of the age of three sister is 68 years. Four year ago the ratio of their ages are 3:4:7. Find the age of the middle sister after 5 years.

October 4th, 2007, 12:22 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
So four years ago their ages were 12, 16, and 28, and at present their ages are 16, 20 and 32. Add 5 onto whichever set of ages you think the question is referring to or just the age of the "middle" sister if you know which one that is.

October 4th, 2007, 07:16 PM  #3 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
We can either solve this math problem using some arithmetic, or both in arithmetic and algebraic terms. I'll pick both arithmetic and algebraic. At present, there were three sisters. One sister is a years old, second sister is b years old, and the third sister is c years old. Therefore, we have a+b+c=68 years. Four years ago, the three sisters' age were a4years, b4years, and c4years. Thus, the total age of the three sisters four years ago is (a4years)+(b4years)+(c4years)=68 years12 years=56 years. Add all the numbers up in the ratio... which is 3+4+7=14. Divide 56 years by 14, which givew 4. Therefore, we have three sisters that have ages of 12 years, 16 years, and 28 years (4 years ago). We can assume any algebraic variable for these numbers, so I'll pick a=16 years, b=20 years, and c=32 years (thus, these are the ages of three sisters' at present). Middle sister is b=20 years (a<b<c), so therefore, after five years, the age of the middle sister is b+5years=20years+5years=25 years. 

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