Kartina has a wheat business. She purchease wheat from a focal wholeselar at a particular cost per pound. The price of the wheat at her stores is $3 per pound . Her faulty spring balance reads 0.9 pounds for a pound. Also , in the festival season, she gives a 10% discount on the wheat. She found that she made neither a profit nor a loss in the festival season. At what price did Katrina purchase the wheat from the wholeselar?

Options

A. 2.43
B. 2.5
C. 2.7
D. 3

Answer

To find the price at which Kartina purchased the wheat from the wholesaler, we can follow these steps:

### Step 1: Understand the Selling Price and Discount
Kartina sells wheat at $3 per pound. During the festival season, she offers a 10% discount on this price.

**Hint:** Calculate the effective selling price after applying the discount.

### Step 2: Calculate the Discounted Selling Price
The discount on the selling price of $3 is calculated as:
\[ \text{Discount} = 10\% \text{ of } 3 = \frac{10}{100} \times 3 = 0.3 \]
Thus, the selling price after the discount is:
\[ \text{Discounted Selling Price} = 3 - 0.3 = 2.7 \]

**Hint:** Remember that the discounted price is what customers pay after the discount is applied.

### Step 3: Account for the Faulty Spring Balance
Kartina's spring balance reads 0.9 pounds for a pound. This means that when she sells what she claims is 1 pound, she is actually giving only 0.9 pounds. Therefore, for every 1 pound sold, the customer receives:
\[ \text{Actual Weight Given} = 1 \text{ pound} + 0.1 \text{ pound} = 1.1 \text{ pounds} \]

**Hint:** Consider how the faulty balance affects the actual quantity of wheat sold.

### Step 4: Calculate the Effective Selling Price per Pound
Since the customer pays $2.7 for what they think is 1 pound, but they actually receive 1.1 pounds, the effective selling price per pound is:
\[ \text{Effective Selling Price} = \frac{2.7}{1.1} \]

**Hint:** Use division to find out how much the customer effectively pays per pound of wheat.

### Step 5: Perform the Calculation
Calculating the effective selling price:
\[ \text{Effective Selling Price} = \frac{2.7}{1.1} = 2.4545 \text{ (approximately)} \]

**Hint:** Round your answer appropriately if necessary.

### Step 6: Determine the Cost Price
Since Kartina made neither a profit nor a loss during the festival season, the cost price (CP) must equal the effective selling price (SP). Thus, we can conclude:
\[ \text{Cost Price} = 2.4545 \]

**Hint:** Remember that if there is no profit or loss, the selling price equals the cost price.

### Final Step: Round to the Given Options
The closest option to our calculated cost price of approximately $2.45 is $2.43.

Thus, the price at which Kartina purchased the wheat from the wholesaler is:
\[ \text{Cost Price} = 2.43 \]

**Final Answer:** $2.43