Video: Writing Linear Equations to Represent a Real-World Context

Both Jacob and Elizabeth love to ride their motorbikes on the mountain roads. If Jacob rode 24 more miles than Elizabeth did, and he rode 38 miles in total, write an equation that describes the number of miles 𝑣 that Elizabeth rode.

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Video Transcript

Both Jacob and Elizabeth love to ride their motorbikes on the mountain roads. If Jacob rode 24 more miles than Elizabeth did, and he rode 38 miles in total, write an equation that describes the number of miles 𝑣 that Elizabeth rode.

We know that Jacob rode 38 miles in total. Elizabeth rode for 𝑣 miles. We’re also told that Jacob rode for 24 miles more than Elizabeth. This means that when we add 24 miles to Elizabeth’s distance, we get an answer of 38 miles. This can be written as the following equation. 𝑣 plus 24 is equal to 38. An equation that describes the number of miles 𝑣 that Elizabeth rode is 𝑣 plus 24 equals 38.

Whilst we’re not asked to in this question, we could calculate the value of 𝑣, the distance that Elizabeth rode, by solving the equation. In order to do this, we can subtract 24 from both sides. 24 minus 24 is equal to zero. So, the left-hand side simplifies to 𝑣. 38 minus 24 is equal to 14. Therefore, 𝑣 is equal to 14. We can therefore conclude that Elizabeth rode for 14 miles.

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