Question

The number of men and women receiving bachelors degrees each year has been steadily increasing. For the years 1970 through the projection of 2014, the number of men receiving degrees ( in thousands ) is given by the equation y=3.7+441, and for women, the equation is y=14.4+314, where x is the number of years after 1970 A. Use the substitution method to solve the system of equations Sketch a graph of the system of equations, write a sentence describing the trends for men and women receiving bachelor degrees

Answer 1

a. x = 12

b. 12 years after 1970, the number of men graduating equals the number of women graduating.

c.

Step-by-step explanation:

We have the system

`\begin{gathered} y=3.7x+441 \\ y=14.4x+314 \end{gathered}`

and we solve it by substituting the value of y from the first equation into the second equation:

`14.4x+314=3.7x+441`

subtracting 314 from both sides gives

`14.4x=3.7x+127`

subtracting 3.7 from both sides gives

`10.7x=127`

Finally, dividing both sides by 127 gives

`x=(127)/(10.7)`
`\boxed{x=11.869\ldots}`

which rounded to the nearest whole number is

`\boxed{x=12}`

The solution tells us that 12 years after 1970, the number of men graduating equals the number of women graduating.

The graph of the equations is given below:

By looking at the slope we see that more women graduate than men and after 12 years, the number of graduating women is greater than men.