In finding the unknown number we used a box: $6 \times \square = 42$. Mathematicians often use a letter instead of a box. The letter is just a number we have not found yet.
Why it works
A letter lets you write a story as an equation before you know the answer. "Some packs of 6 cards make 42 cards" becomes $p \times 6 = 42$, where $p$ is the number of packs. Now the story is a missing-factor question, and you already know how to answer those.
Key idea
Pick a letter for the number you want. Write the story as an equation. Then find the number that makes the equation true, and check it.
Worked example: From a story
Ana has some packs of cards. Each pack has 6 cards. She has 42 cards. How many packs?
- Let $p$ be the number of packs.
- Packs times cards in a pack makes the total: $p \times 6 = 42$.
- $7 \times 6 = 42$, so $p = 7$.
- Check: 7 packs of 6 is 42 cards.
Answer: $p = 7$ packs
Worked example: A letter being divided
Find $n$: $n \div 4 = 6$.
- $n$ shared into 4 groups gives 6 in each.
- So $n$ is 4 groups of 6: $n = 4 \times 6 = 24$.
- Check: $24 \div 4 = 6$.
Answer: $n = 24$
Common mistake
Treating the letter as a word. In $p \times 6 = 42$, $p$ is not "packs." It is the number of packs, 7. Write your answer as $p = 7$, and say what it means: 7 packs.