Question

section 4.2 part - to - part ratios
objective 1 - understand part - to - part ratios
objective 2 - evaluate concentrations
objective 1 - understand part - to - part ratios
guided practice activity #3 - parts of the pop
the following table gives sizes of the u.s. population on july 1, 2017
(https://www.census.gov/data/datasets/2017/demo/popest/nation - detail.html).

1. compute the total, and then fill in the rest of the ratio table given the different quantities that

have been set to 100. make sure to always use the numbers in the first row to avoid round -
off error. note the header row with titles is not counted as the \first\ row.

1. use each of the 4 numbers from the first column in a sentence. one sentence for each

number, and interpret the as both rates per 100 and as percentages for the three rates.

Explanation:

Part 1: Compute the total and fill the ratio table

Step 1: Calculate the total population

To find the total population, we sum the number of people in each age group: Under 18 years, 18 to 64 years, and 65 years and over.

$$ \text{Total} = 73,655,378 + 201,205,121 + 50,858,679 $$

First, add \(73,655,378 + 201,205,121 = 274,860,499\). Then add \(274,860,499 + 50,858,679 = 325,719,178\). So the total population is \(325,719,178\).

Step 2: Fill the row where "18 to 64 years" is 100.0 (ratio per 100 of 18 - 64 group)

We need to find the ratio of each group to the "18 to 64 years" group. For "Under 18 years":

$$ \text{Ratio} = \frac{73,655,378}{201,205,121} \times 100 \approx 36.61 $$

For "65 years and over":

$$ \text{Ratio} = \frac{50,858,679}{201,205,121} \times 100 \approx 25.28 $$

For "Total": Since the "18 to 64 years" group is 100, the total ratio is \(\frac{325,719,178}{201,205,121} \times 100 \approx 161.89\) (but since we are using the first row numbers, and the total is the sum, but in terms of ratio to 18 - 64, it's the sum of the ratios: \(36.61 + 100 + 25.28 \approx 161.89\), but we can also calculate directly as above).

Step 3: Fill the row where "65 years and over" is 100.0 (ratio per 100 of 65+ group)

For "Under 18 years":

$$ \text{Ratio} = \frac{73,655,378}{50,858,679} \times 100 \approx 144.82 $$

For "18 to 64 years":

$$ \text{Ratio} = \frac{201,205,121}{50,858,679} \times 100 \approx 395.61 $$

For "Total":

$$ \text{Ratio} = \frac{325,719,178}{50,858,679} \times 100 \approx 640.43 $$

Step 4: Fill the row where "Total" is 100 (percentage of total)

For "Under 18 years":

$$ \text{Percentage} = \frac{73,655,378}{325,719,178} \times 100 \approx 22.61 $$

For "18 to 64 years":

$$ \text{Percentage} = \frac{201,205,121}{325,719,178} \times 100 \approx 61.77 $$

For "65 years and over":

$$ \text{Percentage} = \frac{50,858,679}{325,719,178} \times 100 \approx 15.61 $$

Filled Table:

Under 18 years	18 to 64 years	65 years and over	Total
~36.61	100.0	~25.28	~161.89
~144.82	~395.61	100.0	~640.43
~22.61	~61.77	~15.61	100

Part 2: Sentences for each number in the first column (Under 18 years: 73,655,378; ~36.61; ~144.82; ~22.61)

1. For 73,655,378:

The number of people under 18 years in the U.S. on July 1, 2017, was 73,655,378.

1. For ~36.61 (ratio per 100 of 18 - 64 group):

For every 100 people in the 18 - 64 years age group, there are approximately 36.61 people under 18 years (or 36.61% of the 18 - 64 group is under 18 years).

1. For ~144.82 (ratio per 100 of 65+ group):

For every 100 people in the 65 years and over age group, there are approximately 144.82 people under 18 years (or 144.82% of the 65+ group is under 18 years).

1. For ~22.61 (percentage of total):

Approximately 22.61% of the total U.S. population on July 1, 2017, was under 18 years (or for every 100 people in the total population, about 22.61 are under 18 years).

Answer:

(Part 1 Table Summary):
The total population is \(325,719,178\). The filled ratio table (rounded to two decimal places) is as shown above.

(For Part 2, the sentences are as constructed above to interpret each number in the first column.)