When a group of colleagues discussed where their annual retreat should take place, they found that of all the colleagues: 17 would not go to a park, 24 would not go to a beach, 13 would not go to a cottage, 8 would go to neither a park nor a beach, 3 would go to neither a beach nor a cottage, 2 would go to neither a park nor a cottage, 1 would not go to a park or a beach or a cottage, and 8 were willing to go to all three places. what is the total number of colleagues in the group?

765238725478629038640962136509762139056074

step-by-step explanation:

64087235609746097215074621039754021037

delaney would like to make a 5lb nut mixture that is 60% peanuts and 40% almonds.

she has several pounds of peanuts and several pounds of a mixture that is 20% peanuts and 80% almonds.

let 'p' represent the number of pounds of peanuts needed to make the new mixture, and  

let 'm' represent the number of pounds of the 80% almond-20% peanut mixture.

:

p + m = 5

therefore

m = (5-p)

write an equation based on the percent of peanuts

1p + .2m = .6(5)

replace m with (5-p)

p + .2(5-p) = .6(5)

p + 1 - .2p = 3

p - .2p = 3 - 1

.8p = 2

p = 2/.8

p = 2.5 lbs of peanuts required

then

5 - 2.5 = 2.5 lbs of the peanut/almond mixture required

:

a) what is the system that models this situation?

p + m = 5

1p + .2m = .6(5)