Question

according to statistics, a person will devote 33 years to sleeping and watching tv. the number of years sleeping will exceed the number of years watching tv by 19. over the lifetime, how many years will the person spend on each of these activities? the person will spend □ years watching tv and □ years sleeping. (type whole numbers.)

Explanation:

Step1: Define variables

Let \( x \) be the number of years watching TV, and \( y \) be the number of years sleeping.
We have two equations:

1. \( x + y = 33 \) (total years for both activities)
2. \( y = x + 19 \) (sleeping years exceed TV years by 19)

Step2: Substitute the second equation into the first

Substitute \( y = x + 19 \) into \( x + y = 33 \):
\( x + (x + 19) = 33 \)
Simplify: \( 2x + 19 = 33 \)

Step3: Solve for \( x \)

Subtract 19 from both sides: \( 2x = 33 - 19 = 14 \)
Divide by 2: \( x = \frac{14}{2} = 7 \)

Step4: Solve for \( y \)

Using \( y = x + 19 \), substitute \( x = 7 \):
\( y = 7 + 19 = 26 \)

Answer:

The person will spend \( 7 \) years watching TV and \( 26 \) years sleeping.