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Rita baked 33 tomes as many chocolate cookies as butter cookies. After selling 6060 chocolate cookies and 1212 butter cookies, there were 33 times as many butter cookies as chocolate cookies. How many chocolate cookies did Rita bake at first?

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Full solution

Q. Rita baked 33 tomes as many chocolate cookies as butter cookies. After selling 6060 chocolate cookies and 1212 butter cookies, there were 33 times as many butter cookies as chocolate cookies. How many chocolate cookies did Rita bake at first?
  1. Define Variables: Let the number of butter cookies be bb. Then, the number of chocolate cookies is 3b3b, since Rita baked 33 times as many chocolate cookies as butter cookies.
  2. Calculate Remaining Cookies: After selling 6060 chocolate cookies and 1212 butter cookies, Rita has 3b−603b - 60 chocolate cookies and b−12b - 12 butter cookies left.
  3. Set Up Equation: According to the problem, after selling the cookies, there were 33 times as many butter cookies as chocolate cookies. So, we can write the equation: b−12=3(3b−60)b - 12 = 3(3b - 60).
  4. Solve Equation: Now, we solve the equation: b−12=9b−180b - 12 = 9b - 180.
  5. Combine Like Terms: Bring all the bb terms to one side: b−9b=−180+12b - 9b = -180 + 12.
  6. Simplify Equation: Simplify the equation: −8b=−168-8b = -168.
  7. Find Value of b: Divide both sides by −8-8 to find the value of bb: b=−168−8b = \frac{-168}{-8}.
  8. Calculate Number of Chocolate Cookies: Calculate the value of bb: b=21b = 21.
  9. Calculate Number of Chocolate Cookies: Calculate the value of bb: b=21b = 21.Now that we know the number of butter cookies, we can find the initial number of chocolate cookies, which is 33 times bb: 3×21=633 \times 21 = 63 chocolate cookies.

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