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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 18. Over the lifetime, how many years will the person spend on each of these activities?

The person will spend
(Type whole numbers.

years watching TV and

years sleeping.

1 answer

Let's denote the number of years a person spends watching TV as \( x \) and the number of years spent sleeping as \( y \).

According to the problem, we have two pieces of information:

  1. The total years spent on sleeping and watching TV is 34 years: \[ x + y = 34 \]

  2. The number of years sleeping exceeds the number of years watching TV by 18 years: \[ y = x + 18 \]

Now we can substitute the second equation into the first equation. Replacing \( y \) in the first equation with \( x + 18 \): \[ x + (x + 18) = 34 \]

Combining like terms: \[ 2x + 18 = 34 \]

Now, we'll isolate \( x \) by subtracting 18 from both sides: \[ 2x = 34 - 18 \] \[ 2x = 16 \]

Dividing both sides by 2: \[ x = 8 \]

Now that we have \( x \), we can find \( y \) using the second equation: \[ y = x + 18 \] \[ y = 8 + 18 \] \[ y = 26 \]

Thus, the person will spend:

  • 8 years watching TV
  • 26 years sleeping

So the final answer is:

The person will spend 8 years watching TV and 26 years sleeping.