Bailey's Boutique Clothing is having a 20% off sale during which shirts cost $30.00 and pants cost $60.00. On the day of the sale, Bailey's sells a total of 60 shirts and pants and earned a total of $2,250. On a regular day, Bailey's sells `2/3` the number of shirts and pants sold during the sale and earns a total of $1,875. Solving which of the following system of equations yields the number of shirts,s, and the number of pants,p, sold during a regular day?

Options

A. `s+p=40`
`37.5s+75p=1,875`
B. `s+p=40`
`30s+60p=2,250`
C. `s+p=60`
`30s+60p=2,250`
D. `s+p=2,250`
`30s+60p=60`

Answer

To solve the problem, we need to establish the equations based on the information provided about the sale and the regular day sales at Bailey's Boutique Clothing.

### Step 1: Determine the equations for the sale day
1. **Total items sold during the sale:**
- Let \( s \) be the number of shirts sold and \( p \) be the number of pants sold.
- According to the problem, the total number of shirts and pants sold during the sale is 60.
- Therefore, we can write the first equation as:
\[ s + p = 60 \]

2. **Total revenue earned during the sale:**
- Shirts are sold for $30 each and pants for $60 each.
- The total revenue from selling shirts and pants during the sale is $2,250.
- Thus, we can write the second equation as:
\[ 30s + 60p = 2250 \]

### Step 2: Determine the equations for a regular day
1. **Total items sold on a regular day:**
- It is given that on a regular day, Bailey's sells \( \frac{2}{3} \) of the total items sold during the sale.
- Therefore, the total number of shirts and pants sold on a regular day is:
\[ s + p = \frac{2}{3} \times 60 = 40 \]

2. **Total revenue earned on a regular day:**
- We need to find the regular prices of shirts and pants.
- Since shirts are sold at a 20% discount for $30, the original price \( X \) of a shirt can be calculated as follows:
\[ X - 0.2X = 30 \implies 0.8X = 30 \implies X = \frac{30}{0.8} = 37.5 \]
- Similarly, for pants sold at a 20% discount for $60:
\[ Y - 0.2Y = 60 \implies 0.8Y = 60 \implies Y = \frac{60}{0.8} = 75 \]
- Therefore, the revenue equation for a regular day, where \( s \) shirts and \( p \) pants are sold, is:
\[ 37.5s + 75p = 1875 \]

### Step 3: Formulate the system of equations
Now we have the following system of equations for a regular day:
1. \( s + p = 40 \)
2. \( 37.5s + 75p = 1875 \)

### Conclusion
The correct system of equations that yields the number of shirts \( s \) and the number of pants \( p \) sold during a regular day is:
1. \( s + p = 40 \)
2. \( 37.5s + 75p = 1875 \)