Video: Creating Linear Equations with One Variable

Let 𝑛 represent an unknown number. Write an equation that represents the statement β€œSixteen more than two-thirds of an unknown number is thirty-six.”

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Video Transcript

Let 𝑛 represent an unknown number. Write an equation that represents the statement β€œ16 more than two-thirds of an unknown number is 36.”

The unknown number in this question is represented by 𝑛, and we want two-thirds of this number. This can be written as two-thirds multiplied by 𝑛 or two-thirds 𝑛. As we want 16 more than this, we need to add 16. This gives us two-thirds 𝑛 plus 16. We’re told this is equal to 36, so two-thirds 𝑛 plus 16 is equal to 36. This is the equation that represents the given statement.

Whilst we don’t need to in this question, we could then solve the equation to calculate the value of 𝑛. This could be done using the balancing method and inverse operations. We could firstly subtract 16 from both sides of the equation. This would give us two-thirds of 𝑛 is equal to 20 as 36 minus 16 is 20. Finally, we could divide both sides of the equation by two-thirds.

The left-hand side would become 𝑛 as two-thirds 𝑛 divided by two-thirds is 𝑛. Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. This means that 20 divided by two-thirds is the same as 20 multiplied by three-halves or three over two. 20 multiplied by three is 60 and dividing this by two gives us 30. The value of 𝑛 that satisfies the equation is 30.

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