https://file.aiquickdraw.com/mathbot/file/17289296710086726j859.jpg

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 $ s $ be the cost of one scarf, and $ h $ be the cost of one hat.

We can set up the following system of equations based on the given information:

1. $ 4s + 6h = 52 $  (Equation for the total cost of 4 scarves and 6 hats)
2. $ 2h = s + 1 $   (Equation stating that the cost of two hats is $1 more than one scarf)

### Solving the system:

**Step 1: Solve the second equation for $ s $:**

From $ 2h = s + 1 $, solve for $ s $:
\[
s = 2h - 1
\]

**Step 2: Substitute this expression into the first equation:**

Substitute $ s = 2h - 1 $ into $ 4s + 6h = 52 $:
\[
4(2h - 1) + 6h = 52
\]
Simplify:
\[
8h - 4 + 6h = 52
\]
\[
14h - 4 = 52
\]
\[
14h = 56
\]
\[
h = 4
\]

**Step 3: Find $ s $:**

Substitute $ h = 4 $ into $ s = 2h - 1 $:
\[
s = 2(4) - 1 = 8 - 1 = 7
\]

### 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:

1. How can you check the solution for both equations in the system?
2. Can you solve this problem using a different approach, such as graphing?
3. How would the problem change if the cost of two hats were $2 more than one scarf?
4. Can this system be solved using substitution or elimination differently?
5. 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.

The cost of four scarves and six hats is $52. The cost of two hats is $1 more than the cost of one scarf. What are the costs of one scarf and one hat?

Learn how to solve a system of equations involving the cost of scarves and hats. This problem teaches algebra concepts such as substitution and linear equations, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation