Chapter A.9, Problem 109AYU

To determine

To find: The Social Security Administration determined that an average 30-year-old male in 2015 could expect to live at least $52.3$ more years and that an average 30-year-old female in 2015 could expect to live at least $55.8$ more years.

a. what age could an average 30-year-old male expect to live? Express your answer as an inequality.

b. what age could an average 30-year-old female expect to live? Express your answer as an inequality.

c. Who can expect to live longer, a male or a female? By how many years?

Answer to Problem 109AYU

a. male $\ge$ $82.3$ years

b. female $\ge$ $85.8$ years

c. the female expect to live longer by $3.5$ years.

Explanation of Solution

Given:

The Social Security Administration determined that an average 30-year-old male in 2015 could expect to live at least $52.3$ more years and that an average 30-year-old female in 2015 could expect to live at least $55.8$ more years.

Calculation:

a. Given that $30$ year old male in 2014 could expect to live atleast $52.3$ more year.

∴ $\text{The expectation of living years of male }= 30 + 52.3 = 82.3$

$\text{i.e.}, \text{male} \ge 82.3 \text{years}$

b. Given that average 30 year old female in 2014 could expect to live atleast $55.8$ years and more.

∴ $\text{The expectation of living years of female }= 30 + 55.8 = 85.8$

$\text{i.e.}, \text{female} \ge 85.8 \text{years}$

c. From $\left(\text{a}\right)$ and $\left(\text{b}\right)$, we can say that the female expect to live longer by $$ 3.5$$ years.

$\left(\because 85.8 - 82.3 = 3.7\right)$