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?

We can let x be the number of boxes sold for the first week. We can as well express the number of boxes for the second and third week through x using the statements provided.

Since the girl scout sold 5 more boxes on the second week, we have (x + 5) number of boxes sold for the second week. Now, for the third week, since it's double that of the second week, we have 2(x + 5). Thus, we have the following:

first week: x
second week: x + 5
third week: 2(x + 5)

Given that the total number of boxes sold for the three weeks is 431. We have

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

We have now the value of x. Using this, we can find the values for the second and third week.
x + 5 = `104 + 5 = 109
2(x + 5) = 2(109) = 218

 
first week: 104
second week: 109
third week: 218

The third and fourth box.