The relationship described can be formulated as an inverse variation, which means that if one variable increases, the other decreases proportionally. Mathematically, this can be represented as:
\[ x \cdot y = k \]
where \( x \) is the age of the person, \( y \) is the number of hours spent on the smart device per week, and \( k \) is a constant.
Given:
- For a 20-year-old ( \( x = 20 \) ), \( y = 52 \) hours: \[ 20 \cdot 52 = k \ k = 1040 \]
Now, we need to find the number of hours a 50-year-old ( \( x = 50 \) ) spends on their smart device. We can plug \( x \) into the formula and solve for \( y \):
\[ 50 \cdot y = 1040 \]
To solve for \( y \):
\[ y = \frac{1040}{50} \ y = 20.8 \]
Thus, a 50-year-old person spends 20.8 hours on their smart device each week.
The answer is 20.8 hours.
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