Question

the table below shows the percentage of male and female populations in a certain country employed in the civilian work - force in selected years from 1970 to 2005. algebraically, the linear model for the female data is $y_1 = 0.493x+28.9$ and the linear model for the male data is $y_2=-0.603x + 84.1$, where the 1970 and 2000 ordered pairs are used to compute the slopes. if the percentages continue to follow the linear models, at what point will the lines intersect? what is the significance of the intersection point in terms of employment participation?
year 1970 1975 1980 1985 1990 1995 2000 2005
female (%) 28.9 31.2 33.5 36.6 40.0 42.3 43.7 42.1
male (%) 84.1 80.6 78.7 75.2 68.3 65.7 63.6 65.5
(type an ordered pair. round to the nearest tenth as needed.)
what is the significance of the intersection point in terms of employment participation? select the correct choice below and fill in the answer box to complete your choice.
a. the linear models suggest that, at the intersection point, female and male participation rates will be different in the year
(round down to the nearest year.)
b. the linear models suggest that, at the intersection point, female and male participation rates will be the same in the year
(round down to the nearest year.)

Explanation:

Step1: Set the two linear - equations equal

We have the linear equation for female data $y_1 = 0.493x+28.9$ and for male data $y_2=-0.603x + 84.1$. Set $y_1=y_2$.
So, $0.493x+28.9=-0.603x + 84.1$.

Step2: Solve for $x$

First, add $0.603x$ to both sides of the equation:
$0.493x+0.603x+28.9=-0.603x+0.603x + 84.1$.
$1.096x+28.9 = 84.1$.
Then, subtract 28.9 from both sides:
$1.096x+28.9 - 28.9=84.1 - 28.9$.
$1.096x=55.2$.
Finally, divide both sides by 1.096:
$x=\frac{55.2}{1.096}\approx50.4$.

Step3: Find the value of $y$

Substitute $x = 50.4$ into the equation $y_1 = 0.493x+28.9$.
$y=0.493\times50.4+28.9$.
$y = 0.493\times50.4+28.9=24.8472+28.9=53.7472\approx53.7$.
The ordered - pair is $(50.4,53.7)$.

The year corresponding to $x$ is $1970 + 50.4\approx2020$ (rounded down to the nearest year).

Answer:

$(50.4,53.7)$
B. The linear models suggest that, at the intersection point, female and male participation rates will be the same in the year 2020.