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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) 5m+3=12m5m + 3 = 12m\newline(B) 3m+12=5m3m + 12 = 5m\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) 5m+3=12m5m + 3 = 12m\newline(B) 3m+12=5m3m + 12 = 5m\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 is icing cookies.\newline- Colette has a head start of 1212 cookies and ices at a rate of 33 cookies per minute.\newline- Max ices at a rate of 55 cookies per minute.\newlineWe want to find the point where the number of cookies iced by Max equals the number of cookies iced by Colette.\newlineColette's cookies can be represented by the equation: 3m+123m + 12 (since she starts with 1212 and ices 33 per minute).\newlineMax's cookies can be represented by the equation: 5m5m (since he ices 55 per minute).\newlineWe set these two equations equal to each other to find when Max catches up to Colette:\newline3m+12=5m3m + 12 = 5m
  2. Set Equations Equal: Now we need to solve for mm.\newlineSubtract 3m3m from both sides to get the mm terms on one side:\newline3m+12−3m=5m−3m3m + 12 - 3m = 5m - 3m\newline12=2m12 = 2m
  3. Solve for mm: Next, we divide both sides by 22 to isolate mm:122=2m2\frac{12}{2} = \frac{2m}{2}6=m6 = m
  4. Isolate mm: So, Max will catch up to Colette after 66 minutes.

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