Chapter 6.1, Problem 22PPS

a)

To determine

To express: The ratio of people ages 0-17 to the people ages 18-30 as a fraction in simplest form.

Answer to Problem 22PPS

The ratio of people ages 0-17 to the people ages 18-30 as a fraction in simplest form is $\frac{1}{3}$ .

Explanation of Solution

Given information: 

Given the following table, showing different age groups shop the departmental store:

  

Concept used:

A ratio between two said age groups will be set as a fraction by putting first age group number in numerator and second age group numbers in denominator and then dividing it by common factor to put this fraction in simplest form.

Conclusion:

As total numbers in age group 0-17 be 25 and in ages 18-30 be 75, so it’s ratio is calculated as follows:

  $\Rightarrow \frac{25}{75}=\frac{1}{3}$

So, ratio is $\frac{1}{3}$ .

b)

To determine

To express: The ratio of people ages 0-30 to the people ages 30 or more as a fraction in simplest form.

Answer to Problem 22PPS

The ratio of people ages 0-30 to the people ages 30 or more as a fraction in simplest form is $\frac{5}{4}$ .

Explanation of Solution

Given information: Given the following table, showing different age groups shop the departmental store:

  

Concept used: A ratio between two said age groups will be set as a fraction by putting first age group number in numerator and second age group numbers in denominator and then dividing it by common factor to put this fraction in simplest form.

Conclusion:

As total numbers in age group 0-30 is,

  $\Rightarrow 25+75=100$

And total numbers over ages 30 is,

  $\Rightarrow 54+26=80$

As total numbers in age group 0-30 be 100 and in ages 31+ be 80, so it’s ratio is calculated as follows:

  $\Rightarrow \frac{100}{80}=\frac{5}{4}$

So, required ratio asked, in simplest form is $\frac{5}{4}$ .

c)

To determine

To express: The ratio of people ages 18-30 to the total number of people as a fraction in simplest form.

Answer to Problem 22PPS

Ratio of people ages 18-30 to the total number of people as a fraction in simplest form is $\frac{5}{12}$ .

Explanation of Solution

Given information: Given the following table, showing different age groups shop the departmental store:

  

Concept used: A ratio between two said age groups will be set as a fraction by putting first age group number in numerator and second age group numbers in denominator and then dividing it by common factor to put this fraction in simplest form.

Conclusion: As total numbers in age group 18-30 be 75 and total people be 180, so its said ratio:

  $\frac{75}{180}=\frac{5}{12}$

So, required ratio in simplest form is $\frac{5}{12}$ .