One's intelligence quotient, or IQ, varies directly as a person's mental age and inversely as that person's chronological age. A person with a mental age of 20 and a chronological age of 20 has an IQ of 140 . What is-the chronological age of a person with a mental age of 35 and an IQ of 140 ? The chronological age is

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UpStudy AI · Accepted Answer

Assume that a person's IQ, denoted by $$ \text{IQ} $$, is given by the formula

$$
\text{IQ} = k \left(\frac{\text{mental age}}{\text{chronological age}}\right)
$$

for some constant $$ k $$.

**Step 1: Find the constant $$ k $$.**

Given a person with a mental age of 20 and a chronological age of 20 has an IQ of 140, substitute these values into the formula:

$$
140 = k \left(\frac{20}{20}\right)
$$

Simplify:

$$
140 = k \cdot 1 \quad \Rightarrow \quad k = 140
$$

**Step 2: Set up the equation for the new person.**

For a person with a mental age of 35 and an IQ of 140, substitute the known values:

$$
140 = 140 \left(\frac{35}{\text{chronological age}}\right)
$$

**Step 3: Solve for the chronological age.**

Divide both sides of the equation by 140:

$$
1 = \frac{35}{\text{chronological age}}
$$

Solve for the chronological age:

$$
\text{chronological age} = 35
$$

Thus, the chronological age is $$ \boxed{35} $$.
The chronological age is 35.

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