DA Sixth-grade class salls candy and soda. They earn 5 profit tor each soda and 43 profi for each candy sold. They sell t00 iHems in tetal for a prfit of $135. What system of. éamations represents these reiationships, where c represents candy and s represents soda ?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem Statement:**

A sixth-grade class sells candy and soda. They earn $5 profit for each soda and $3 profit for each candy sold. They sell 100 items in total for a profit of $385. What system of equations represents these relationships, where \( c \) represents candy and \( s \) represents soda?

**Solution Steps:**

1. **Identify the Variables:**
   - Let \( c \) represent the number of candies sold.
   - Let \( s \) represent the number of sodas sold.

2. **Equations:**
   - Total items sold equation: \( c + s = 100 \)
   - Total profit equation: \( 3c + 5s = 385 \)

3. **Solve the System of Equations:**
   - **Equation 1:** \( c + s = 100 \)
   - **Equation 2:** \( 3c + 5s = 385 \)

4. Use substitution or elimination to solve these equations (not detailed here).

**Additional Problem:**

- **What is the solution to the system?**
  - \( y = x + 3 \)
  - \( -3x + 2y = 6 \)

- **Solution Steps for the Additional Problem:**
  - Substitute \( y = x + 3 \) into the second equation.
  - Solve for \( x \) and \( y \) using appropriate algebraic methods.

**Solution Box:**

- The solution is provided as \((13)\).

(Note: The boxed solution in the image seems to be a shorthand, likely referring to a set of values for \( x \) and \( y \), such as \( (1, 3) \) although the full context or clarity may vary.)

The image does not contain graphs or diagrams, so no visual descriptions are necessary.
Transcribed Image Text:**Problem Statement:** A sixth-grade class sells candy and soda. They earn $5 profit for each soda and $3 profit for each candy sold. They sell 100 items in total for a profit of $385. What system of equations represents these relationships, where \( c \) represents candy and \( s \) represents soda? **Solution Steps:** 1. **Identify the Variables:** - Let \( c \) represent the number of candies sold. - Let \( s \) represent the number of sodas sold. 2. **Equations:** - Total items sold equation: \( c + s = 100 \) - Total profit equation: \( 3c + 5s = 385 \) 3. **Solve the System of Equations:** - **Equation 1:** \( c + s = 100 \) - **Equation 2:** \( 3c + 5s = 385 \) 4. Use substitution or elimination to solve these equations (not detailed here). **Additional Problem:** - **What is the solution to the system?** - \( y = x + 3 \) - \( -3x + 2y = 6 \) - **Solution Steps for the Additional Problem:** - Substitute \( y = x + 3 \) into the second equation. - Solve for \( x \) and \( y \) using appropriate algebraic methods. **Solution Box:** - The solution is provided as \((13)\). (Note: The boxed solution in the image seems to be a shorthand, likely referring to a set of values for \( x \) and \( y \), such as \( (1, 3) \) although the full context or clarity may vary.) The image does not contain graphs or diagrams, so no visual descriptions are necessary.
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