a girl 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?
Let x = first week, then x+5 = second and 2(x+5) = third week. They should sum to 431.
Solve for x.
To solve this problem, let's break it down step by step.
Step 1: Define the variables.
Let's call the number of boxes sold in the first week "x".
Since the girls sold 5 more boxes the second week than they did the first week, the number of boxes sold in the second week can be represented as "x + 5".
The number of boxes sold in the third week will be twice the sales of the second week, so we can represent it as "2(x + 5)".
Step 2: Set up the equation.
The total number of boxes sold is given as 431. So we can set up the equation:
x + (x + 5) + 2(x + 5) = 431
Step 3: Solve the equation.
Combine like terms on the left side of the equation:
x + x + 5 + 2x + 10 = 431
4x + 15 = 431
Subtract 15 from both sides of the equation:
4x = 431 - 15
4x = 416
Divide both sides of the equation by 4:
x = 416/4
x = 104
Step 4: Calculate the number of boxes sold each week.
Now that we know the value of "x", we can substitute it back into the equations we created earlier to find the number of boxes sold each week:
- First week: x = 104 boxes sold
- Second week: x + 5 = 104 + 5 = 109 boxes sold
- Third week: 2(x + 5) = 2(109) = 218 boxes sold
So, the girl scout troop sold 104 boxes in the first week, 109 boxes in the second week, and 218 boxes in the third week.