# Video: Creating Linear Equations with One Variable

Michael and Elizabeth are competing on a quiz app. Michael has 40 points already and is winning 20 points per minute. Elizabeth has 20 points already and is winning 25 points per minute. Write an equation that can be used to find 𝑚, the number of minutes until Elizabeth overtakes Michael.

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### Video Transcript

Michael and Elizabeth are competing on a quiz app. Michael has 40 points already and is winning 20 points per minute. Elizabeth has 20 points already and is winning 25 points per minute. Write an equation that can be used to find 𝑚, the number of minutes until Elizabeth overtakes Michael.

As Michael has 40 points already and is winning 20 points per minute, his total points will be given by 40 plus 20𝑚. Elizabeth has 20 points already and is winning 25 points per minute. Therefore, her total points will be given by 20 plus 25𝑚. This means that the equation that can be used to find the number of minutes until Elizabeth overtakes Michael is 20 plus 25𝑚 is equal to 40 plus 20𝑚.

Whilst we weren’t ask to solve this equation, we could do so using the balancing method. Subtracting 20 from both sides of the equation gives us 25𝑚 is equal to 20 plus 20𝑚. Subtracting 20𝑚 from both sides of this new equation gives us five 𝑚 is equal to 20. And finally, dividing both sides of this by five gives us 𝑚 is equal to four. This means that, after four minutes, both players, Michael and Elizabeth, will be on 120 points. After this point, Elizabeth will overtake Michael.