The formula I = 100M/C can be used.I range of a group of 9-year-olds is given by 90 = I = 170

Question

A person's intelligence quotient (I) is found by dividing mental age (M), as indicated by standard tests, by chronological age (C) and then multiplying this ratio by 100. Find the range of the mental age of this group.

solve the problem by setting up and solving an appropriate inequality. I just need help with setting up and finding what numbers to use. 

Answer 1

Arielle ... This is a challenging question. The range is given as an inequality

and the answer is an inequality. But the solution is not found by solving the

inequality - that's over thinking the problem. It's much simpler. Simply solve

both ends of of the inequality to get the end values of the inequality which

 answers your problem.

 

Formula: I =  100M/C   Known Variables: C = 9 yrs old

 

I_MIN <= I <= I_MAX   so  90 <= I <= 170

 

I_MIN =  100*M_MIN/9 = 90                  I_MAX = 100*M_MAX/9 = 170

 

         9*100*M_MIN/9 = 9*90             9*100*M_MAX/9 = 9*170

 

            100 M_MIN = 810                  100M_MAX = 1530

 

            M_MIN = 8.1                         M_MAX = 15.3

 

Answer as an inequality:  8.1 <= M <= 15.3 .

 

Answer as a complete sentence:  "The mental range of the group of 9 year olds with IQs ranging from 90 to 170 is 8.1 years to 15.3 years old."