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In the final round of the Western Baking Challenge, Max and Colette must each create a display of iced cookies. Colette's cookies cooled off first, and she begins icing them at a rate of 33 cookies per minute. After Collette has iced 1212 cookies, Max starts icing his cookies at a rate of 55 cookies per minute. Soon, he will catch up to Colette and the two will have iced the same number of cookies.\newlineWhich equation can you use to find mm, the number of minutes it will take Max to catch up to Colette?\newlineChoices:\newline(A) 3m+12=5m3m + 12 = 5m\newline(B) 5m+3=12m5m + 3 = 12m\newlineHow long will it take Max to catch up to Colette?\newlineSimplify any fractions.\newline____ minutes\newline

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Q. In the final round of the Western Baking Challenge, Max and Colette must each create a display of iced cookies. Colette's cookies cooled off first, and she begins icing them at a rate of 33 cookies per minute. After Collette has iced 1212 cookies, Max starts icing his cookies at a rate of 55 cookies per minute. Soon, he will catch up to Colette and the two will have iced the same number of cookies.\newlineWhich equation can you use to find mm, the number of minutes it will take Max to catch up to Colette?\newlineChoices:\newline(A) 3m+12=5m3m + 12 = 5m\newline(B) 5m+3=12m5m + 3 = 12m\newlineHow long will it take Max to catch up to Colette?\newlineSimplify any fractions.\newline____ minutes\newline
  1. Define Variables: Let's define the variables:\newline- Let mm be the number of minutes Max ices cookies.\newline- Colette has a head start of 1212 cookies and ices at a rate of 33 cookies per minute.\newline- Max ices cookies at a rate of 55 cookies per minute.\newlineWe want to find when Max will have iced the same number of cookies as Colette. To do this, we need to set up an equation that represents the total number of cookies iced by each person.\newlineColette's cookies: 1212 (head start) + 3m3m (rate of icing per minute times the number of minutes).\newlineMax's cookies: 5m5m (rate of icing per minute times the number of minutes).\newlineThe equation to represent when they will have iced the same number of cookies is:\newline3m+12=5m3m + 12 = 5m\newlineNow we need to solve for mm.
  2. Set Up Equation: Subtract 3m3m from both sides of the equation to get the mm terms on one side:\newline3m+12−3m=5m−3m3m + 12 - 3m = 5m - 3m\newlineThis simplifies to:\newline12=2m12 = 2m
  3. Solve Equation: Now, divide both sides by 22 to solve for mm:122=2m2\frac{12}{2} = \frac{2m}{2}This gives us:m=6m = 6
  4. Final Answer: So, it will take Max 66 minutes to catch up to Colette.

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