Jackson and Sarah are collecting gems in the online multiplayer game Blaze Beams. Jackson joins early and earns $3$ gems per minute. He gathers $36$ gems by the time Sarah joins. Sarah, the more experienced player, earns $7$ gems per minute. Soon, she catches up to Jackson and the two have the same number of gems. $\newline$ Which equation can you use to find $m$ , the number of minutes it takes for Sarah to catch up to Jackson? $\newline$ Choices: $\newline$ (A) $36 + 3m = 7m$ $\newline$ (B) $3m + 7 = 36m$ $\newline$ How long does it take Sarah to catch up to Jackson? $\newline$ Simplify any fractions. $\newline$ ____ minutes $\newline$

Full solution

Q. Jackson and Sarah are collecting gems in the online multiplayer game Blaze Beams. Jackson joins early and earns

3

gems per minute. He gathers

36

gems by the time Sarah joins. Sarah, the more experienced player, earns

7

gems per minute. Soon, she catches up to Jackson and the two have the same number of gems.

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Which equation can you use to find

m

, the number of minutes it takes for Sarah to catch up to Jackson?

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Choices:

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(A)

36 + 3m = 7m

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(B)

3m + 7 = 36m

\newline

How long does it take Sarah to catch up to Jackson?

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Simplify any fractions.

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____ minutes

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Identify Equation: Question Prompt: How long does it take for Sarah to catch up to Jackson in collecting gems?
Solve Equation: Step $1$ : Identify the correct equation to represent the situation. $\newline$ Jackson has a head start of $36$ gems and earns $3$ gems per minute. Sarah earns $7$ gems per minute. The equation to find when Sarah catches up to Jackson is: $\newline$ $36 + 3m = 7m$ , where $m$ is the number of minutes after Sarah starts playing.
Divide and Solve: Step $2$ : Solve the equation $36 + 3m = 7m$ . Subtract $3m$ from both sides to isolate terms with $m$ on one side: $36 = 4m$ .
Divide and Solve: Step $2$ : Solve the equation $36 + 3m = 7m$ . Subtract $3m$ from both sides to isolate terms with $m$ on one side: $36 = 4m$ . Step $3$ : Divide both sides by $4$ to solve for $m$ . $\frac{36}{4} = m$ , $m = 9$ .