The number of boxes of cookies sold by Imelda was 22 fewer than the number of boxes of cookies sold by Sarah. The number of boxes of cookies sold by Keiko was 24 less than the number sold by Sarah. Write an algebraic expression for each quantity. Use x to represent the unknown value.

Let's represent the unknown number of boxes of cookies sold by Sarah with \( x \).

1. **Imelda's cookies sold**: According to the problem, Imelda sold 22 fewer boxes than Sarah. This can be written as:
   \[
   \text{Imelda's cookies} = x - 22
   \]

2. **Keiko's cookies sold**: The problem states that Keiko sold 24 fewer boxes than Sarah. This can be written as:
   \[
   \text{Keiko's cookies} = x - 24
   \]

In summary:
- Sarah's boxes: \( x \)
- Imelda's boxes: \( x - 22 \)
- Keiko's boxes: \( x - 24 \)

Would you like to see how this could be used to set up an equation, or any further details on how to work with these expressions?

Here are 5 questions to deepen your understanding:
1. How would you calculate the total number of boxes sold if you knew the value of \( x \)?
2. What happens if Sarah sold 50 boxes? How many did Imelda and Keiko sell?
3. Can you set up an equation if you know the total number of boxes sold by all three?
4. How would the expression change if Keiko sold 5 more boxes than Sarah instead of 24 fewer?
5. If Imelda sold twice the number of cookies than Sarah, what would the expression for Imelda's sales look like?

**Tip**: When translating word problems into algebraic expressions, always start by defining the unknown with a variable, then build relationships from the given conditions.

Learn how to write algebraic expressions for the number of cookies sold by Imelda and Keiko, who sold fewer cookies than Sarah. This problem helps students understand algebraic concepts like variables and linear equations, suitable for Grades 6-8.

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