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?

they sold boxes the first week, boxes the second week, and boxes the third week.

So,

We have three placeholders.

x, y, and z will represent the number of cookie boxes they sold for the first, second, and third weeks, respectively.

"The girls sold 5 more boxes the second week than they did the first."
x + 5 = y

"They doubled the sales of the second week for the third week."
z = 2y

"To sell a total of 431 boxes of cookies"
x + y + z = 431

Now we have our three equations.
x + 5 = y
z = 2y
x + y + z = 431

Obviously, we can substitute y and z in the last equation, because the other two open sentences tell us what they are.
x + (x + 5) + 2(x + 5) = 431
x + x + 5 + 2(x + 5) = 431

Collect Like Terms.
2x + 5 + 2(x + 5) = 431

Distribute.
2x + 5 + 2x + 10 = 431

Collect Like Terms.
4x + 15 = 431

Subtract 15 from both sides.
4x = 416

Divide both sides by 4.
x = 104

Now we can use the other two original sentences to figure out what y and z are.
x + 5 = y
104 + 5 = y
109 = y

z = 2y
z = 2(109)
z = 218

Now, to check, add x, y, and z.
x + y + z = 431
104 + 109 + 218 = 431
213 + 218 = 431
431 = 431 This checks.

The Girl Scouts sold 104 cookie boxes on the first week, 109 boxes on the second week, and 218 boxes on the third week.