Question

according to statistics, a person will devote 36 years to sleeping and watching tv. the number of years sleeping will exceed the number of years watching tv by 18. 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: Set up equations

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

$$\begin{cases}x + y=36\\y=x + 18\end{cases}$$

\)

Step2: Substitute \(y=x + 18\) into \(x + y=36\)

Substitute \(y\) in the first - equation: \(x+(x + 18)=36\)
Simplify: \(2x+18 = 36\)
Subtract 18 from both sides: \(2x=36 - 18\), so \(2x=18\)
Divide both sides by 2: \(x=\frac{18}{2}=9\)

Step3: Find \(y\)

Since \(y=x + 18\), substitute \(x = 9\) into it. Then \(y=9+18 = 27\)

Answer:

The person will spend \(9\) years watching TV and \(27\) years sleeping.