Answer:
7 members
Step-by-step explanation:
Lets say that the department has n members. If each member contributes with an equal amount x and make a total of $280, we know that:
n*x = 280
Where each one colaborated with:
n*x/n = 280/n
Or what is the same that: (as the n on the left eliminate themselves)
x = 280/n (*)
Now the department hires 3 more members, so we now have n+3 members. And we know that the pass from contributing x to contribute $30 less, it is, x-30 (I omit the $ symbol for simplicity). So, know we have:
x-30 = 280/(n+3)
We can replace x here by the formulation of x we did in the (*) equation:
( 280/n) - 30 = 280/(n+3)
using common denominator:
( 280/n) - 30 n/n = 280/(n+3)
( 280 - 30 n)/n = 280/(n+3)
Cross multiplying the denominators:
( 280 - 30 n)*(n+3) = 280*(n)
280n - 30n^2 + 840 - 90n = 280n
Subtracting 280 n in both sides:
30n^2 + 840 - 90n = 0
Dividing both sides by 30:
-n^2 - 3n + 28 = 0
Factorizing this term (you can notice the factor immediately or solving with baskara resolution, I omit the baskara for simplicity):
-(n + 7)(n - 4) =0
So, n is equal to 4 and -7. As we are dealing with people we can not have -7 people, so we keep only n=4.
So, previous the new hiring there were 4 members, now there are 7.
The used to collaborate with 280/4 = $70, now the collaborate with 280/7=$40, and we see the collaboration decreased in $30.
