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In a group of 14 children some are nine years old and the rest are eleven years old.

In a group of 14 children some are nine years old and the rest are eleven years old. When the ages of the 14 children are added together the total is 138 years. How many nine-year-old children are there? Answer: there are 8 9 year old's but how do you form an algebraic equation to solve the problem? Please and thank you. 
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1 Answer

Flynn,
          Let n11= the number of 11 year olds
          Let n9  = the number of   9 year olds
 
then 11*n11+9*n9= 138    the sum of their ages add up to 138 years
and       n11+    n9=  14     the total number of children adds up to 14
 
if you solve this system of two equations for the two unknowns n11 and n9 you will find n9=8 and n14=6
 
Jim