Question

1-6 N Literal Equations Algebra 1 5) The formula H = 4 is sometimes used to relate a person's age, A, to the number of hours of sleep, H, they need every day. a) Does this formula work for you?

Answer 1

The expression that is used is:

$H=\frac{34-A}{2}$

b) For what ages does the formula seems to work best?

For ages equal or greater than 34, the answer is either 0 or negative, therefore it doesn't work well for those. We know that the sleeping time for humans is usually around 8h, so let's find which ages result in that value:

$\begin{gathered} 8=\frac{34-A}{2} \\ 16=34-A \\ A=34-16 \\ A=18 \end{gathered}$

It seems that the formula works best for values around 18 years old.

c) Solve the value for A

To solve an equation for a given variable we need to isolate said variable on the left side. This is done below:

$\begin{gathered} H=\frac{34-A}{2} \\ 2H=34-A \\ A=34-2H \end{gathered}$

d) To find the age of a person who sleeps 8 h per hour we need to make H=8. We have:

$\begin{gathered} A\text{ = 34-2}\cdot8=34-16 \\ A=18 \end{gathered}$