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

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

Step 2

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

$k=\frac{12}{10}=1.2$

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

$\begin{gathered} H\text{ }=\text{ 1.2 }\times24 \\ H=28.8\text{inches} \end{gathered}$