Let's break down the given information step by step to form a mathematical sentence that represents the situation.
1. Identify the Variables
- Let \( s \) denote the cost of a pair of socks.
2. Analyze the Relationship
- According to the problem, a T-shirt costs 4 times as much as a pair of socks. This can be expressed mathematically as:
[tex]\[
\text{Cost of T-shirt} = 4 \times \text{Cost of socks}
\][/tex]
- Given that a T-shirt costs \(\$ 16\), we can incorporate this into the equation:
[tex]\[
16 = 4 \times s
\][/tex]
3. Form the Equation
- Rearrange the equation to show the relationship more clearly:
[tex]\[
4s = 16
\][/tex]
Now, we can compare this equation with the given options to find the correct one:
A. \( \frac{s}{16}=4 \)
- This implies that the cost of socks is \( \frac{16}{4} \), which is incorrect.
B. \( 16 s = 4 \)
- This implies that the cost of socks would be \( \frac{4}{16} \), which is also incorrect.
C. \( 4 s = 16 \)
- This correctly expresses the relationship: A T-shirt costs 4 times the price of a pair of socks, and the cost of the T-shirt is \(\$ 16\).
D. \( \frac{s}{4}=16 \)
- This implies that the cost of a pair of socks is 64, which is incorrect.
Therefore, the correct mathematical sentence that expresses the given information is:
[tex]\[
4s = 16
\][/tex]
Thus, the correct option is:
C. [tex]\( 4 s=16 \)[/tex]
