Chapter 5.5, Problem 10IP

To determine

Tofind:The missing entries in the given table and constant of proportionality if the set of numbers is proportional.

Answer to Problem 10IP

The missing entries are filled in complete table (1). The set of numbers isproportional and the constant of proportionality is $\frac{2}{5}$ .

Explanation of Solution

Given information:Every 2 students have 5 slices of pizza.

Number of students	2	4	6	8	10
Slices of pizza

Calculation:

It is given that every 2 students has 5 slices of pizza. So, the pizza slice that 4 students can have is:

  $\begin{array}{c}2\text{students}=5\text{slices}\\ 4\text{students}=2\times 5\text{slices}\\ =10\text{slices}\end{array}$

The pizza slice that 6 students can have is:

  $\begin{array}{c}2\text{students}=5\text{slices}\\ 2\times 3\text{students}=3\times 5\text{slices}\\ 6\text{students}=15\text{slices}\end{array}$

The pizza slice that 8 students can have is:

  $\begin{array}{c}2\text{students}=5\text{slices}\\ 4\times 2\text{students}=4\times 5\text{slices}\\ 8\text{students}=20\text{slices}\end{array}$

The pizza slice that 10 students can have is:

  $\begin{array}{c}2\text{students}=5\text{slices}\\ 2\times 5\text{students}=5\times 5\text{slices}\\ 10\text{students}=25\text{slices}\end{array}$

The missing data is filled in the table given below:

Number of students	2	4	6	8	10
Slices of pizza	5	10	15	20	25

Table (1)

The ratio of set of numbers in column 2 is $\frac{2}{5}$ .

The ratio of set of numbers in column 3 is:

  $\frac{4}{10}=\frac{2}{5}$

The ratio of set of numbers in column 4 is:

  $\frac{6}{15}=\frac{2}{5}$

The ratio of set of numbers in column 5 is:

  $\frac{8}{20}=\frac{2}{5}$

The ratio of set of numbers in column 6 is:

  $\frac{10}{25}=\frac{2}{5}$

Therefore, the missing entries are filled in complete table (1). The set of numbers is proportional and the constant of proportionality is $\frac{2}{5}$ .