Question

IQ of a person is given by the formula \(IQ = \frac{MA}{CA}×100, \)  Where MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years old children, find the range of their mental age.

Answer 1

Given:

IQ = (MA / CA) × 100

Chronological age, CA = 12 years

Given range of IQ:

80 ≤ IQ ≤ 140

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Step 1: Substitute CA = 12 in the formula

IQ = (MA / 12) × 100

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Step 2: Form the inequality

80 ≤ (MA / 12) × 100 ≤ 140

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Step 3: Simplify the inequality

Divide throughout by 100:

0.8 ≤ MA / 12 ≤ 1.4

Multiply throughout by 12:

9.6 ≤ MA ≤ 16.8

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Final Answer:

The range of mental age of the children is:
9.6 years ≤ MA ≤ 16.8 years