A recent census revealed the age distribution of the residents of Town Y, shown in the graph. Since the census...

Owning the Dataset

Table 1: Text Analysis

Table 2: Chart Analysis

Key Insights

1. There are approximately 2.65 times as many children or teenagers (45%) as seniors (17%) in the town.
2. People aged 0–39 make up 68% of the total population, while those 40 or above make up 32%.
3. If the difference between these groups is 540 residents, then the total population at the time of the census was 1,500.
4. The population conditions (no migration, births, or deaths) mean these proportions are stable and relevant for all calculations.

Step-by-Step Solution

Question 1: Ratio of Children or Teenagers to Seniors

Complete Statement:

The census indicates that [BLANK] times as many residents were children or teenagers as were seniors.

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: children or teenagers
    • Meaning: This refers to residents in the combined age groups of children (0-12 years) and teenagers (13-19 years).
    • Relation to Chart: The chart shows children as 20% and teenagers as 25% of the total population.
    • Important Implications: We need to combine these two percentage groups for our calculation.
• Statement Breakdown 2:
  • Key Phrase: times as many ... as were seniors
    • Meaning: We are looking for how many times larger the number of children or teenagers is compared to the number of seniors.
    • Relation to Chart: Seniors (age 60+) make up 17% of the population in the chart.
    • Important Implications: The required ratio is: (children + teenagers) divided by seniors.
• What is needed: The ratio of children or teenagers to seniors—how many times larger is the young group compared to seniors.

Solution:

• Condensed Solution Implementation:
  Add the percentages of children and teenagers, then divide that sum by the seniors percentage to get the ratio.
• Necessary Data points:
  Children: 20%, Teenagers: 25%, Seniors: 17%.
  • Calculations Estimations:
    Children + Teenagers = \(20\% + 25\% = 45\%\). \(45\% ÷ 17\% = 2.647\), which rounds to 2.65.
  • Comparison to Answer Choices:
    The answer choices are 1.17, 1.47, 2.65, 3.00. Our result, 2.65, matches one of them exactly.

FINAL ANSWER Blank 1: 2.65

Question 2: Calculating Total Population Based on Age Group Difference

Complete Statement:

If, at the time of the census, there were 540 more people aged 0–39 than people aged 40 or greater, then the population of Town Y at the time of the census was [BLANK].

Breaking Down the Statement

• Statement Breakdown 1:
  • Key Phrase: 540 more people aged 0–39 than people aged 40 or greater
    • Meaning: There is a numerical difference of 540 between these two broader age groups.
    • Relation to Chart: Ages 0-39 include children (20%), teenagers (25%), and young adults (23%). Ages 40+ include middle-aged adults (15%) and seniors (17%).
• Statement Breakdown 2:
  • Key Phrase: population of Town Y
    • Meaning: This is asking for the total population number.
    • Relation to Chart: We relate the percentage difference between these age groups to the provided absolute difference to solve for the total number.
• What is needed: The total population of Town Y.

Solution:

• Condensed Solution Implementation:
  Translate the percentage groups into a percent difference (68% - 32% = 36%) and use the fact that this difference corresponds to 540 people to find the total.
• Necessary Data points:
  Ages 0-39: \(20\% + 25\% + 23\% = 68\%\). Ages 40+: \(15\% + 17\% = 32\%\).
  • Calculations Estimations:
    \(68\% - 32\% = 36\%\) of total = 540 people. So, total = \(540 ÷ 0.36 = 1,500\).
  • Comparison to Answer Choices:
    The options are 1,080, 1,500, 2,400, and 4,000. Our calculation matches 1,500.

FINAL ANSWER Blank 2: 1,500

Summary

Blank 1 is answered by calculating a ratio of age-group percentages, while Blank 2 uses the difference between summed percentage groups and relates it to a population difference to solve for the total. Both answers use data directly from the chart.

Question Independence Analysis

The two blanks are independent. Blank 1 is about a ratio of specific groups, and Blank 2 is about the total population using a calculated difference. Neither answer depends on the other.