Math Problem Statement

Chase and Sara went to the candy store. Chase bought 5 pieces of fudge and 3 pieces of gummy worms for a total of $5.70. Sara bought 2 pieces of fudge and 10 pieces of gummy worms for a total of $3.60. Find the cost of fudge and gummy worms.

Solution

The problem you uploaded asks to solve for the cost of fudge (denoted as ff) and gummy worms (denoted as gwgw) based on two transactions:

  1. Chase bought 5 pieces of fudge and 3 pieces of gummy worms for a total of $5.70. This gives the equation: 5f+3gw=5.705f + 3gw = 5.70

  2. Sara bought 2 pieces of fudge and 10 pieces of gummy worms for a total of $3.60. This gives the equation: 2f+10gw=3.602f + 10gw = 3.60

We now have a system of linear equations:

1. \quad 5f + 3gw &= 5.70 \\ 2. \quad 2f + 10gw &= 3.60 \end{aligned}$$ Let's solve this system of equations to find the values of $$f$$ (cost of fudge) and $$gw$$ (cost of gummy worms). I'll proceed with solving it now.The cost of one piece of fudge $$f$$ is $1.05, and the cost of one piece of gummy worms $$gw$$ is $0.15. Would you like a detailed explanation of the steps involved in solving this system? Here are five related questions you can explore: 1. How can systems of equations be solved using substitution or elimination methods? 2. What are the different types of solutions for systems of linear equations (e.g., unique, infinite, or no solution)? 3. How do you interpret the solution of a system of equations in real-world contexts? 4. What other methods exist for solving systems of equations, such as graphing or matrices? 5. Can this same approach be applied to solve systems of equations with more than two variables? **Tip:** When solving systems of equations, substitution works well when one variable is easy to isolate, while elimination is often more efficient when both equations are similarly structured.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Systems of Equations

Formulas

Linear equation: ax + by = c

Theorems

None

Suitable Grade Level

Grades 7-9

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