https://file.aiquickdraw.com/mathbot/file/1727704186086skz0fy9o.pdf

Let me provide solutions to some of the key problems from the document. I will solve each in turn:

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### **1. Which equation represents the sentence: "Four times the sum of a number x and a number y is equal to 25"?**
We need to express this statement mathematically.

- The sum of \(x\) and \(y\) is \(x + y\).
- Four times the sum is \(4(x + y)\).
- This is equal to 25, so the equation becomes:  
\[
\boxed{4(x + y) = 25}
\]

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### **2. Match each equation to its verbal description:**

- \(3(x + y) = 6\) is "The product of three and the sum of \(x\) and \(y\) is equal to six."
- \(3xy = 6\) is "The product of three times \(x\) and \(y\) is equal to six."
- \(3x + y = 6\) is "The sum of three times \(x\) and \(y\) is equal to six."
- \(3 + xy = 6\) is "The sum of three and the product of \(x\) and \(y\) is equal to six."

Thus, the matching is:
- (a) \( \rightarrow 3(x + y) = 6 \)
- (b) \( \rightarrow 3xy = 6 \)
- (c) \( \rightarrow 3x + y = 6 \)
- (d) \( \rightarrow 3 + xy = 6 \)

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### **3. Write a sentence for the equation \(2 + 3n = 5n\):**
This can be described as:  
"The sum of two and three times a number \(n\) is equal to five times the number."

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### **4. Write an equation for the sentence: "The difference of twice \(x\) and four times the quantity \(x + y\) is equal to ten."**

- Twice \(x\) is \(2x\).
- Four times the quantity \(x + y\) is \(4(x + y)\).
- The difference of these is:  
\[
2x - 4(x + y)
\]
- It is equal to ten, so the full equation is:  
\[
\boxed{2x - 4(x + y) = 10}
\]

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### **5. Write a sentence for the equation \(7(3 + 5n) = an\):**

This equation represents:  
"Seven times the sum of three and five times a number \(n\) is equal to \(an\)."

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Would you like further explanations or solutions to more questions? Here are five follow-up problems that expand on these:

1. Solve the equation \(4(x + y) = 25\) for \(x\) when \(y = 3\).
2. Write a verbal description for the equation \(5(x - 2) + 3 = 20\).
3. Solve the equation \(2x - 4(x + y) = 10\) when \(y = 1\).
4. What is the value of \(n\) that satisfies \(2 + 3n = 5n\)?
5. Write a verbal description for \(6(2n - 1) = 3n + 12\).

**Tip:** When translating sentences into equations, remember that "times" usually indicates multiplication and "the sum of" indicates addition.

Learn how to solve key algebraic equations, including representing verbal statements as equations. Explore examples such as '4(x + y) = 25' and '2x - 4(x + y) = 10'. Suitable for students in Grades 7-9.

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