Question

a. according to statistics, a person will devote 34 years to sleeping and watching tv. the number of years sleeping will exceed the number of years watching tv by 22. over the lifetime, how many years will the person spend on each of these activities?

Explanation:

Step1: Define variables

Let \( x \) be the number of years spent watching TV, and \( y \) be the number of years spent sleeping.

Step2: Set up equations

We know two things:

1. The total years for sleeping and watching TV is 34, so \( x + y = 34 \).
2. The years sleeping exceed watching TV by 22, so \( y = x + 22 \).

Step3: Substitute and solve

Substitute \( y = x + 22 \) into \( x + y = 34 \):
\( x+(x + 22)=34 \)
Simplify: \( 2x+22 = 34 \)
Subtract 22 from both sides: \( 2x=34 - 22=12 \)
Divide by 2: \( x=\frac{12}{2}=6 \)

Step4: Find y

Substitute \( x = 6 \) into \( y = x + 22 \): \( y=6 + 22 = 28 \)

Answer:

The person will spend 6 years watching TV and 28 years sleeping.