Answer :
To solve the problem of finding the cost, [tex]\( c \)[/tex], of each painting class, we need to understand the payment breakdown for Rosanne. We know the following:
1. The total amount paid by Rosanne is \[tex]$186.
2. This total includes the cost of 8 painting classes and a beginner's painting kit priced at \$[/tex]42.
Let's use this information to form an equation. The equation should express the sum of the cost of 8 painting classes and the painting kit as the total amount paid.
The cost of each class is [tex]\( c \)[/tex], so the cost for 8 classes would be [tex]\( 8c \)[/tex].
Now, add the cost of the painting kit to this amount:
[tex]\[ 8c + 42 = 186 \][/tex]
This equation correctly represents the total cost paid by Rosanne. Now let's see which option corresponds to this equation:
- [tex]\( 42(c + 8) = 186 \)[/tex] - This implies 42 is multiplied by [tex]\( (c + 8) \)[/tex], which does not fit the scenario.
- [tex]\( 8(c + 42) = 186 \)[/tex] - This implies that each class costs [tex]\( c + 42 \)[/tex], which is incorrect.
- [tex]\( 42c + 8 = 186 \)[/tex] - This implies the cost of 42 classes plus 8, which is incorrect.
- [tex]\( 8c + 42 = 186 \)[/tex] - This correctly represents the total cost as the sum of the cost of 8 classes and the cost of the kit.
Therefore, the correct equation to find the cost, [tex]\( c \)[/tex], of each painting class is:
[tex]\[ 8c + 42 = 186 \][/tex]
1. The total amount paid by Rosanne is \[tex]$186.
2. This total includes the cost of 8 painting classes and a beginner's painting kit priced at \$[/tex]42.
Let's use this information to form an equation. The equation should express the sum of the cost of 8 painting classes and the painting kit as the total amount paid.
The cost of each class is [tex]\( c \)[/tex], so the cost for 8 classes would be [tex]\( 8c \)[/tex].
Now, add the cost of the painting kit to this amount:
[tex]\[ 8c + 42 = 186 \][/tex]
This equation correctly represents the total cost paid by Rosanne. Now let's see which option corresponds to this equation:
- [tex]\( 42(c + 8) = 186 \)[/tex] - This implies 42 is multiplied by [tex]\( (c + 8) \)[/tex], which does not fit the scenario.
- [tex]\( 8(c + 42) = 186 \)[/tex] - This implies that each class costs [tex]\( c + 42 \)[/tex], which is incorrect.
- [tex]\( 42c + 8 = 186 \)[/tex] - This implies the cost of 42 classes plus 8, which is incorrect.
- [tex]\( 8c + 42 = 186 \)[/tex] - This correctly represents the total cost as the sum of the cost of 8 classes and the cost of the kit.
Therefore, the correct equation to find the cost, [tex]\( c \)[/tex], of each painting class is:
[tex]\[ 8c + 42 = 186 \][/tex]
