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Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter9: Systems Of Linear Equations
Section9.3: Solving Problems With Two Variables
Problem 18P
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**Educational Content: Solving Linear Equations**

---

**Problem Statement:**

Terry buys beads by the bag to make jewelry. There are 25 beads in each bag. Which equation can he use to find the number of beads in any number of bags if:

- \( n \) equals any number of bags, and
- \( t \) equals the total number of beads?

---

**Options Provided:**

1. \( 25t = n \)
2. \( 25 + n = t \)
3. \( 25n = t \)
4. \( 25 + t = n \)

---

**Explanation:**

To find the correct equation that relates the number of bags of beads and the total number of beads, consider the following:

- Each bag has 25 beads.
- If you have \( n \) bags, then the total number of beads would be \( 25 \) beads multiplied by the number of bags \( n \).

Hence, the correct equation that represents this relationship is \( 25n = t \).

This equation indicates that multiplying the number of bags \( n \) by 25 (the number of beads in each bag) gives the total number of beads \( t \).

**Selecting the Correct Answer:**

From the options given, the third option, \( 25n = t \), is the correct equation.

---

**Summary:**

To determine the total number of beads in any given number of bags, simply use the equation \( 25n = t \), where \( n \) is the number of bags and \( t \) is the total number of beads.

**Interactive Element:**

Students can practice more problems of a similar type or use interactive tools to enter different values for \( n \) to dynamically see the resulting total number of beads \( t \).

---
Transcribed Image Text:**Educational Content: Solving Linear Equations** --- **Problem Statement:** Terry buys beads by the bag to make jewelry. There are 25 beads in each bag. Which equation can he use to find the number of beads in any number of bags if: - \( n \) equals any number of bags, and - \( t \) equals the total number of beads? --- **Options Provided:** 1. \( 25t = n \) 2. \( 25 + n = t \) 3. \( 25n = t \) 4. \( 25 + t = n \) --- **Explanation:** To find the correct equation that relates the number of bags of beads and the total number of beads, consider the following: - Each bag has 25 beads. - If you have \( n \) bags, then the total number of beads would be \( 25 \) beads multiplied by the number of bags \( n \). Hence, the correct equation that represents this relationship is \( 25n = t \). This equation indicates that multiplying the number of bags \( n \) by 25 (the number of beads in each bag) gives the total number of beads \( t \). **Selecting the Correct Answer:** From the options given, the third option, \( 25n = t \), is the correct equation. --- **Summary:** To determine the total number of beads in any given number of bags, simply use the equation \( 25n = t \), where \( n \) is the number of bags and \( t \) is the total number of beads. **Interactive Element:** Students can practice more problems of a similar type or use interactive tools to enter different values for \( n \) to dynamically see the resulting total number of beads \( t \). ---
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