Chapter 12, Problem 13QC

To determine

To calculate:To determine whether the set of numbers in the table are proportional and explain the reasoning

Answer to Problem 13QC

Set of numbers are in proportion

Explanation of Solution

Given information:Table with set of numbers:

Bottles	1	2	3	4
Cost ($)	1.25	2.50	3.75	5.00

Formula Used: Proportion is a statement when two ratios are equal. It can be written in two ways:

  $\frac{a}{b}=\frac{c}{d}$ or $a:b=c:d$

Also, if the cross product two ratios are equal, then ratios are in Proportion

Calculation:

Set of numbers are given as follows:

Bottles	1	2	3	4
Cost ($)	1.25	2.50	3.75	5.00

Ratios are given as follows:

  $\frac{1}{1.25}$ , $\frac{2}{2.50}$ , $\frac{3}{3.75}$ , $\frac{4}{5.00}$

Let us find the simplest form of each ratio:

  $\frac{1}{1.25}=\frac{1}{1.25}$

  $\frac{2}{2.50}=\frac{1}{1.25}$

  $\frac{3}{3.75}=\frac{1}{1.25}$

  $\frac{4}{5.00}=\frac{1}{1.25}$

Here, $\frac{1}{1.25}=\frac{2}{2.50}=\frac{3}{3.75}=\frac{4}{5.00}$

Since the cross product of ratios are equal, thus the set of numbers are in proportion

Conclusion:

Hence, set of numbers are in proportion