MATH SOLVE

2 months ago

Q:
# The enrollment in college a may be modeled by y = 0.051x + 0.470, and the enrollment in college b may be modeled by y = –0.041x + 1.850, where x is the number of years since 1990 and y is the enrollment in thousands. when will the two colleges have the same enrollment and what is that enrollment?

Accepted Solution

A:

The first equation represents the enrollments of college A

The second equation represents the enrollments of college B

if you let two equation equal to each other, you can understand them as the enrollments of college A and college B at "x" year.

0.051x + 0.470 = -0.041x + 1.850

0.051x + 0.041x = 1.850 - 0.470

0.092x = 1.38

x = 1.38/0.092 = 15 years from 1990, 1990 + 15 = 2005

both equations represents the enrollments, but for specific the year of 2005, they have the same enrollments. You can either plug 2005 in the first or second equation, the answer will come out the same.

y = 0.051(2005) + 0.470 = 102.745 thousands of enrollments. It's awkward to say it this way, you can multiply 102.745 by 1000.

==> 102.725 * 1000 = 102725 enrollements

===================================================================

The year of 2005 college A and college B both have the same enrollments of 102725.

The second equation represents the enrollments of college B

if you let two equation equal to each other, you can understand them as the enrollments of college A and college B at "x" year.

0.051x + 0.470 = -0.041x + 1.850

0.051x + 0.041x = 1.850 - 0.470

0.092x = 1.38

x = 1.38/0.092 = 15 years from 1990, 1990 + 15 = 2005

both equations represents the enrollments, but for specific the year of 2005, they have the same enrollments. You can either plug 2005 in the first or second equation, the answer will come out the same.

y = 0.051(2005) + 0.470 = 102.745 thousands of enrollments. It's awkward to say it this way, you can multiply 102.745 by 1000.

==> 102.725 * 1000 = 102725 enrollements

===================================================================

The year of 2005 college A and college B both have the same enrollments of 102725.