College

Principal Jordan ordered 65 cupcakes from Sweet Sue's Bakery for his monthly honor roll party. Since this was a bulk order, Sweet Sue's reduced the price of each cupcake by [tex]$0.50[/tex]. Principal Jordan paid [tex]$195[/tex] in all.

Which equation can you use to find [tex]c[/tex], how much Sweet Sue's normally charges for a cupcake?

A. [tex]65c - 0.50 = 195[/tex]
B. [tex]0.50c - 65 = 195[/tex]
C. [tex]0.50(c - 65) = 195[/tex]
D. [tex]65(c - 0.50) = 195[/tex]

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]