# IQ of a person is given by the formula $IQ= \large\frac{MA}{CA} $$\times 100 Where MA is a mental age and CA is chronological age. If 80 \leq IQ \leq 140 for a group of 12 years old children find the range of their mental age . ## 1 Answer Toolbox: • Same Quantity can be added (a subtracted ) to (from ) both sides of the inequality with out changing the sign of the in equality. • Same positive quantities can be multiplied or divided to both side of the in equality with out changing the sign of the inequality. • If same negative quantity is multiplied or divided to both sides of the inequality is reversed i.e '>' sign changes to '<' and '<' changes '>' . For a group of 12 years old children the chronological age CA=12 years The given group of 12 years old children has 80 \leq IQ \leq 140 Substituting IQ = \large\frac{MA}{12}$$\times 100 \leq 140$----(1)
Multiplying by positive number $\large\frac{12}{100}$ through out the inequality we get,
=> $80 \times \large\frac{12}{100} \leq \large\frac{MA}{12} $$\times 100 \times \large\frac{12}{100}$$ \leq 140 \times \large\frac{12}{100}$
=> $9.6 \leq MA \leq 16.8$
Thus we see that the range of metal age of 12 years old children is more than or equal to 9.6 and less than or equal to 16.8
The solution set is $9.6 \leq MA \leq 16.8$