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Answer :
To solve this problem, we need to set up an equation that reflects the given scenario. Let's break down the problem step-by-step.
1. Identify Variables:
- Let [tex]\( c \)[/tex] be the normal price of one cupcake in dollars.
2. Given Information:
- Principal Jordan ordered 65 cupcakes.
- Sweet Sue's Bakery reduced the price of each cupcake by [tex]$0.50.
- Principal Jordan paid a total of $[/tex]195.
3. Form the Equation:
- The normal cost of one cupcake is [tex]\( c \)[/tex] dollars.
- After the discount, the price of one cupcake becomes [tex]\( c - 0.50 \)[/tex] dollars.
- For 65 cupcakes, the total cost paid is given by [tex]\( 65 \times (c - 0.50) \)[/tex].
4. Total Cost:
- This total cost should equal the amount Principal Jordan paid, which is [tex]$195.
Therefore, the equation can be written as:
\[ 65(c - 0.50) = 195 \]
This equation correctly represents the scenario.
5. Solution:
To illustrate how we might solve this equation:
\[ 65(c - 0.50) = 195 \]
First, distribute \( 65 \):
\[ 65c - 65 \times 0.50 = 195 \]
\[ 65c - 32.50 = 195 \]
Next, isolate \( c \):
\[ 65c = 195 + 32.50 \]
\[ 65c = 227.50 \]
Finally, solve for \( c \):
\[ c = \frac{227.50}{65} \]
\[ c = 3.50 \]
So Sweet Sue's normally charges \( \$[/tex]3.50 \) per cupcake.
### Validate the Correct Equation
The correct equation among the given options is:
[tex]\[ 65(c - 0.50) = 195 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{65(c - 0.50) = 195} \][/tex]
1. Identify Variables:
- Let [tex]\( c \)[/tex] be the normal price of one cupcake in dollars.
2. Given Information:
- Principal Jordan ordered 65 cupcakes.
- Sweet Sue's Bakery reduced the price of each cupcake by [tex]$0.50.
- Principal Jordan paid a total of $[/tex]195.
3. Form the Equation:
- The normal cost of one cupcake is [tex]\( c \)[/tex] dollars.
- After the discount, the price of one cupcake becomes [tex]\( c - 0.50 \)[/tex] dollars.
- For 65 cupcakes, the total cost paid is given by [tex]\( 65 \times (c - 0.50) \)[/tex].
4. Total Cost:
- This total cost should equal the amount Principal Jordan paid, which is [tex]$195.
Therefore, the equation can be written as:
\[ 65(c - 0.50) = 195 \]
This equation correctly represents the scenario.
5. Solution:
To illustrate how we might solve this equation:
\[ 65(c - 0.50) = 195 \]
First, distribute \( 65 \):
\[ 65c - 65 \times 0.50 = 195 \]
\[ 65c - 32.50 = 195 \]
Next, isolate \( c \):
\[ 65c = 195 + 32.50 \]
\[ 65c = 227.50 \]
Finally, solve for \( c \):
\[ c = \frac{227.50}{65} \]
\[ c = 3.50 \]
So Sweet Sue's normally charges \( \$[/tex]3.50 \) per cupcake.
### Validate the Correct Equation
The correct equation among the given options is:
[tex]\[ 65(c - 0.50) = 195 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{65(c - 0.50) = 195} \][/tex]
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