Question 274418
Let {{{n}}} = the number of students at N Campus before merger
Let {{{s}}} = the number of students at S Campus before merger
given:
(1) {{{n + s = 100}}}
{{{.5n + .6s = .55*100}}}
{{{.5n + .6s = 55}}}
(2) {{{5n + 6s = 550}}}
Multiply both sides of (1) by {{{5}}} and
subtract (1) from (2)
(2) {{{5n + 6s = 550}}}
(1) {{{-5n - 5s = -500}}}
{{{s = 50}}}
And, from (1),
(1) {{{n + s = 100}}}
{{{n + 50 = 100}}}
{{{n = 50}}}
The N campus had 50 students and the S campus also had 50 students
check answer:
{{{.5n + .6s = .55*100}}}
{{{.5*50 + .6*50 = 55}}}
{{{25 + 30 = 55}}}
OK