Answer :
Sure! Let's solve this step-by-step:
Rosanne paid for an Introduction to Painting course where the cost includes 8 painting classes, and she also bought a beginner's painting kit for \[tex]$42. The total amount she paid is \$[/tex]186. We need to find the cost, [tex]\( c \)[/tex], of each painting class.
Here’s how to set up and solve the equation:
1. Identify the costs involved in the total payment:
- Cost of 8 painting classes.
- Cost of the painting kit.
2. Express these costs in terms of [tex]\( c \)[/tex]:
- Cost of 8 painting classes is [tex]\( 8c \)[/tex].
- Cost of the painting kit is \[tex]$42.
3. Write the equation for the total cost:
- Total cost = Cost of 8 painting classes + Cost of the painting kit
- So, we can write: \( 8c + 42 = 186 \).
Therefore, the equation we use to find the cost \( c \) of each painting class is:
\[ 8c + 42 = 186. \]
This equation will allow us to solve for \( c \). Here is the step-by-step solution:
1. Subtract 42 from both sides of the equation to isolate the term with \( c \):
\[ 8c + 42 - 42 = 186 - 42 \]
\[ 8c = 144 \]
2. Divide both sides by 8 to solve for \( c \):
\[ \frac{8c}{8} = \frac{144}{8} \]
\[ c = 18 \]
So, the cost of each painting class is \( \$[/tex]18 \).
Rosanne paid for an Introduction to Painting course where the cost includes 8 painting classes, and she also bought a beginner's painting kit for \[tex]$42. The total amount she paid is \$[/tex]186. We need to find the cost, [tex]\( c \)[/tex], of each painting class.
Here’s how to set up and solve the equation:
1. Identify the costs involved in the total payment:
- Cost of 8 painting classes.
- Cost of the painting kit.
2. Express these costs in terms of [tex]\( c \)[/tex]:
- Cost of 8 painting classes is [tex]\( 8c \)[/tex].
- Cost of the painting kit is \[tex]$42.
3. Write the equation for the total cost:
- Total cost = Cost of 8 painting classes + Cost of the painting kit
- So, we can write: \( 8c + 42 = 186 \).
Therefore, the equation we use to find the cost \( c \) of each painting class is:
\[ 8c + 42 = 186. \]
This equation will allow us to solve for \( c \). Here is the step-by-step solution:
1. Subtract 42 from both sides of the equation to isolate the term with \( c \):
\[ 8c + 42 - 42 = 186 - 42 \]
\[ 8c = 144 \]
2. Divide both sides by 8 to solve for \( c \):
\[ \frac{8c}{8} = \frac{144}{8} \]
\[ c = 18 \]
So, the cost of each painting class is \( \$[/tex]18 \).
