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? They sold _____ boxes the first week, _____ boxes the second week, and ____ boxes the third week.
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.
