It's math smart I need help with some questions
Let p = people in the room and r = room capacity. Here's what we know:
p = 1/2 r (the original # of people filled to half capacity)
p - 10 = ^{1}/_{3} r (after 10 people left, it's now at ^{
1}/_{3} capacity)
We have a value for a variable, so we can plug it in:
^{1}/_{2} r - 10 = ^{1}/_{3} r
Subtract 1/2 r from both sides:
-10 = ^{1}/_{3} r - ^{1}/_{2} r
Find the LCD:
-10 = ^{2}/_{6} r - ^{3}/_{6} r
-10 = -^{1}/_{6} r
Multiply both sides by -^{1}/_{6}:
60 = r
Check:
p = 60 / 2 (the half capacity at the start)
p = 30
30 - 10 = 60 / 3 (the half-cap minus 10 should equal one-third of the full-cap)
20 = 20