Math Problem Statement
Solution
The problem states the following:
- The cost of four scarves and six hats is $52.
- The cost of two hats is $1 more than the cost of one scarf.
Let be the cost of one scarf, and be the cost of one hat.
We can set up the following system of equations based on the given information:
- (Equation for the total cost of 4 scarves and 6 hats)
- (Equation stating that the cost of two hats is $1 more than one scarf)
Solving the system:
Step 1: Solve the second equation for :
From , solve for :
Step 2: Substitute this expression into the first equation:
Substitute into : Simplify:
Step 3: Find :
Substitute into :
Conclusion:
The cost of one scarf is $7, and the cost of one hat is $4.
Thus, the correct answer is D: $7; $4.
Would you like more details or have any questions? Here are 5 follow-up questions to expand your understanding:
- How can you check the solution for both equations in the system?
- Can you solve this problem using a different approach, such as graphing?
- How would the problem change if the cost of two hats were $2 more than one scarf?
- Can this system be solved using substitution or elimination differently?
- How does solving systems of equations apply to real-world problems like budgeting?
Tip: When solving word problems, always define your variables clearly to avoid confusion when setting up equations.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
Systems of Equations
Formulas
4s + 6h = 52
2h = s + 1
Theorems
Substitution method for solving systems of equations
Suitable Grade Level
Grades 6-8
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