Question
The number of weekly hours spent on a smart device varies inversely with the person's age. If a 20-year-old person spends 52 hours on their smart device each week, how many hours does a 50-year-old person spend on their smart device?
98 hours
20.8 hours
130 hours
19.2 hours
98 hours
20.8 hours
130 hours
19.2 hours
Answers
Answered by
GPT-4o mini
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**.
\[
x \cdot y = k
\]
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**.