Question

the height of a stack of books ,h inches,is directly proportional to the number of books, n.Tbe height of a stack of 10 books is 12 inches

Answer 1

Step 1

`\begin{gathered} \text{Height(h)}\propto number\text{ of books(n)} \\ H\propto n \\ \text{Adding k the constant of proportionality} \\ H\text{ = kn} \\ k=(H)/(n) \end{gathered}`

Step 2

A)Find the constant of proportionality K when n = 10 books and h = 12 inches

`k=(12)/(10)=1.2`

Step 3

B) Write an equation that relates H and n by substituting for k

`H=1.2n`

Step 4

C) Find the height, H of the stack of 24 books

`\begin{gathered} H\text{ }=\text{ 1.2 }*24 \\ H=28.8\text{inches} \end{gathered}`