Math Problem Statement
If Sue buys three packets of chips and two bottles of cola, it will cost her $13.20. However, if she buys two packets of chips and three bottles of cola it will cost her only $11.80. What is the price of each item? 90
Solution
Let's solve this problem by setting up a system of linear equations based on the information provided.
Let:
- be the price of one packet of chips.
- be the price of one bottle of cola.
From the problem, we can create the following equations:
Solving the System of Equations
We can use the method of elimination or substitution to solve for and .
Step 1: Multiply both equations to eliminate one variable.
Let's eliminate . Multiply Equation 1 by 2 and Equation 2 by 3:
Step 2: Subtract Equation 3 from Equation 4 to eliminate :
Step 3: Solve for :
So, the price of one bottle of cola is $1.80.
Step 4: Substitute back into Equation 1 to solve for :
So, the price of one packet of chips is $3.20.
Final Answer:
- The price of one packet of chips is $3.20.
- The price of one bottle of cola is $1.80.
Would you like more details on this solution, or do you have any questions?
Here are 8 related questions to consider:
- What if Sue buys 5 packets of chips and 4 bottles of cola? How much will it cost?
- How would the solution change if the prices were different?
- Can you solve a similar problem with different coefficients?
- How would you check if the solution is correct?
- What is the graphical representation of the system of equations?
- Can this problem be solved using matrix methods?
- What are other methods to solve a system of linear equations?
- How would you interpret the solution in terms of real-life scenarios?
Tip: When solving systems of equations, always check your solution by substituting the values back into the original equations to ensure they satisfy both equations.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9