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?

Answer 1

To find the number of hours a 50-year-old person spends on their smart device, we can use the formula for inverse variation. By plugging in the given values, we find that a 50-year-old person spends approximately 20.8 hours on their smart device each week.

Step-by-step explanation:

To solve this problem, we can use the formula for inverse variation which states that the product of the two variables remains constant. In this case, the number of weekly hours spent on a smart device and the person's age are inversely related.

We can express this relationship as follows:

Weekly Hours = k/Age

Where k is the constant of variation.

To find the specific equation for this problem, we can plug in the given values. Let's use the information that a 20-year-old person spends 52 hours on their smart device each week. So, Weekly Hours = 52 and Age = 20. Plugging these values in, we get:

52 = k/20

To solve for k, we can cross-multiply:

k = 52 * 20 = 1040

Now, we have the equation: Weekly Hours = 1040/Age

To find the number of hours a 50-year-old person spends on their smart device, we can plug in Age = 50 into the equation:

Weekly Hours = 1040/50 = 20.8 hours

Therefore, a 50-year-old person spends approximately 20.8 hours on their smart device each week.

Answer 2

20.8 hours

Step-by-step explanation:

Given that hours (h) varies inversely with age (a) then the equation relating them is

h =
`(k)/(a)` ← k is the constant of variation

To find k use the condition h = 52 when a = 20, thus

52 =
`(k)/(20)` ( multiply both sides by 20 )

1040 = k

h =
`(1040)/(a)` ← equation of variation

When a = 50, then

h =
`(1040)/(50)` = 20.8 hours