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Jackson and Sarah are collecting gems in the online multiplayer game Blaze Beams. Jackson joins early and earns 33 gems per minute. He gathers 3636 gems by the time Sarah joins. Sarah, the more experienced player, earns 77 gems per minute. Soon, she catches up to Jackson and the two have the same number of gems.\newlineWhich equation can you use to find mm, the number of minutes it takes for Sarah to catch up to Jackson?\newlineChoices:\newline(A) 3m+7=36m3m + 7 = 36m\newline(B) 36+3m=7m36 + 3m = 7m\newlineHow long does it take Sarah to catch up to Jackson?\newlineSimplify any fractions.\newline____ minutes\newline

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Q. Jackson and Sarah are collecting gems in the online multiplayer game Blaze Beams. Jackson joins early and earns 33 gems per minute. He gathers 3636 gems by the time Sarah joins. Sarah, the more experienced player, earns 77 gems per minute. Soon, she catches up to Jackson and the two have the same number of gems.\newlineWhich equation can you use to find mm, the number of minutes it takes for Sarah to catch up to Jackson?\newlineChoices:\newline(A) 3m+7=36m3m + 7 = 36m\newline(B) 36+3m=7m36 + 3m = 7m\newlineHow long does it take Sarah to catch up to Jackson?\newlineSimplify any fractions.\newline____ minutes\newline
  1. Define variable mm: Let's define the variable mm as the number of minutes it takes for Sarah to catch up to Jackson. Jackson has a head start of 3636 gems and collects 33 gems per minute. Sarah collects 77 gems per minute. The equation to represent the situation where Sarah catches up to Jackson is the total number of gems Jackson has (his head start plus 33 times the number of minutes) equals the total number of gems Sarah collects (77 times the number of minutes).\newlineThe correct equation is:\newline36+3m=7m36 + 3m = 7m
  2. Solve for m: To solve for m, we need to get all the terms with mm on one side and the constants on the other. We can do this by subtracting 3m3m from both sides of the equation.\newline36+3m−3m=7m−3m36 + 3m - 3m = 7m - 3m\newlineThis simplifies to:\newline36=4m36 = 4m
  3. Isolate variable mm: Now, we divide both sides by 44 to isolate mm.364=4m4\frac{36}{4} = \frac{4m}{4}This gives us:m=9m = 9
  4. Check solution: We check our solution by plugging it back into the original equation to ensure it makes sense.\newline36+3(9)=7(9)36 + 3(9) = 7(9)\newline36+27=6336 + 27 = 63\newline63=6363 = 63\newlineThe solution checks out.

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