Agirl scout troop sold cookies. if the girls sold 5 more boxes the second week than they did the first, and if they doubled the sales of the second week for the third week to sell a total of 431 boxes of cookies, how many did they sell each week?

N = first integer 
n + 1 = second integer 
n + 2 = third 
n + 3 = fourth 

the sum is 114 so: 

n + (n + 1) + (n + 2) + (n + 3) = 114 

solve: 

4n + 6 = 114 
4n = 108 
n = 27 

so 27 is your first. 
27 + 1 is your second (remember n +1 n +2 and n +3) 

so your first four integers are: 27 28 29 and 30 

(I'll also help with one) 

week one: x 
week two: x + 5 
week three: 2(x+5) or 2x + 10 

week1 + 2 + 3 = 431 

so its: 

x + (x+5) + (2x + 10) 
4x + 15 = 431 
4x = 416 
x = 104 

its then: 

week one: 104 sold 
week two: 109 sold (x + 5) 
week three: 218 (2x + 10)

The answer is 6 weeks