Let's break down the given expression step by step to find the equivalent expression for the cost of the item.
The initial expression is:
[tex]\[ c - 0.25c \][/tex]
This represents the original cost [tex]\( c \)[/tex] minus [tex]\( 25\% \)[/tex] off.
### Step 1: Understanding [tex]\( 25\% \)[/tex] Off
When you get [tex]\( 25\% \)[/tex] off of an item, it means you are paying [tex]\( 75\% \)[/tex] of the original cost. Mathematically, [tex]\( 25\% \)[/tex] of [tex]\( c \)[/tex] is:
[tex]\[ 0.25c \][/tex]
### Step 2: Subtracting the Discount
To find the final cost after the discount, we subtract [tex]\( 0.25c \)[/tex] from the original cost [tex]\( c \)[/tex]:
[tex]\[ c - 0.25c \][/tex]
### Step 3: Combining Like Terms
Now we need to combine like terms. Both terms in the expression are multiples of [tex]\( c \)[/tex], so we can factor [tex]\( c \)[/tex] out:
[tex]\[ c - 0.25c = (1 - 0.25)c \][/tex]
### Step 4: Simplifying the Expression
We simplify the coefficient:
[tex]\[ 1 - 0.25 = 0.75 \][/tex]
Therefore, the expression simplifies to:
[tex]\[ 0.75c \][/tex]
### Conclusion
The equivalent expression for the cost of the item after a [tex]\( 25\% \)[/tex] discount is:
[tex]\[ 0.75c \][/tex]
Thus, the correct answer from the given options is:
[tex]\[ \boxed{0.75c} \][/tex]
