Answer :
Alright, let’s break down the cost calculation for [tex]$y$[/tex] books step by step.
1. Cost for the first copy: The publisher charges [tex]\(\$ 15\)[/tex] for the first copy.
2. Cost for additional copies: For each additional copy (starting from the second one), the publisher charges [tex]\(\$ 12\)[/tex].
3. Total Cost Calculation:
- If only one book is ordered ([tex]\(y = 1\)[/tex]), the total cost is simply [tex]\(\$ 15\)[/tex].
- If more than one book is ordered ([tex]\(y > 1\)[/tex]), the total cost will include the price for the first book plus the price for the remaining [tex]\(y-1\)[/tex] books.
So, let's represent this in an expression:
- The first book costs [tex]$\$[/tex] 15[tex]$. - Each additional book costs $[/tex]\[tex]$ 12$[/tex].
- If there are [tex]\(y\)[/tex] books in total, the number of additional books is [tex]\(y - 1\)[/tex].
Thus, the total cost can be written as:
[tex]\[ \text{Total cost} = 15 + 12 \times (y - 1) \][/tex]
Now, let’s simplify this expression:
[tex]\[ \text{Total cost} = 15 + 12y - 12 \][/tex]
Combine the constant terms ([tex]\(15 - 12\)[/tex]):
[tex]\[ \text{Total cost} = 12y + 3 \][/tex]
Therefore, the expression that represents the cost of [tex]\(y\)[/tex] books is:
[tex]\[ 12y + 3 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{12y + 3} \][/tex]
The answer choice corresponding to this expression is F.
1. Cost for the first copy: The publisher charges [tex]\(\$ 15\)[/tex] for the first copy.
2. Cost for additional copies: For each additional copy (starting from the second one), the publisher charges [tex]\(\$ 12\)[/tex].
3. Total Cost Calculation:
- If only one book is ordered ([tex]\(y = 1\)[/tex]), the total cost is simply [tex]\(\$ 15\)[/tex].
- If more than one book is ordered ([tex]\(y > 1\)[/tex]), the total cost will include the price for the first book plus the price for the remaining [tex]\(y-1\)[/tex] books.
So, let's represent this in an expression:
- The first book costs [tex]$\$[/tex] 15[tex]$. - Each additional book costs $[/tex]\[tex]$ 12$[/tex].
- If there are [tex]\(y\)[/tex] books in total, the number of additional books is [tex]\(y - 1\)[/tex].
Thus, the total cost can be written as:
[tex]\[ \text{Total cost} = 15 + 12 \times (y - 1) \][/tex]
Now, let’s simplify this expression:
[tex]\[ \text{Total cost} = 15 + 12y - 12 \][/tex]
Combine the constant terms ([tex]\(15 - 12\)[/tex]):
[tex]\[ \text{Total cost} = 12y + 3 \][/tex]
Therefore, the expression that represents the cost of [tex]\(y\)[/tex] books is:
[tex]\[ 12y + 3 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{12y + 3} \][/tex]
The answer choice corresponding to this expression is F.
