Question

The number of licensed male drivers, in thousands, in the U.S. may be modeled by y = 961.98x + 76,820.54, and the number of licensed female drivers, in thousands, in the U.S. may be modeled by y = 1,296.36x + 68,162.65, where x is the number of years since 1980. According to the models, approximately when will the number of licensed male drivers in the U.S. equal the number of licensed female drivers in the U.S.?
A.2006

B.2004

C.2011

D.1954

Answer 1

Answer:

A. 2006

Step-by-step explanation:

Given:

Number of male drivers model by equation $y = 961.98x + 76820.54$

Number of female drivers model by equation $y = 1296.36x + 68162.65$

Where $x$ ⇒ the number of years since 1980

We need to find when will the number of licensed male drivers in the U.S. equal the number of licensed female drivers in the U.S.

Solution:

Now we can say that;

to find number of years when the number of licensed male drivers in the U.S. equal the number of licensed female drivers in the U.S we need to make both the equation equal we get;

$961.98x + 76820.54=1296.36x + 68162.65$

Now Combining the like terms we get;

$1296.36x -961.98x =76820.54- 68162.65\\\\334.38x=8657.89$

Now By using Division property dividing both side by 334.89 we get;

$\frac{334.38x}{334.38}=\frac{8657.89}{334.38}\\\\x= 25.89 \approx 26 years$

Now x is number of years after 1980.

So we can say that;

26 years after 1980 is 2006.

Hence Approximately in the year 2006  the number of licensed male drivers in the U.S. equal the number of licensed female drivers in the U.S.