A spice store charged 2.75 for 25 grams of paprika. It also charges 5% of the purchase price for shipping any order. Write and simplify an expression to determine the cost of buying and shipping x ounces of paprika. Use 1 once = 28 grams Can a customer buy 2.5 ounces of paprika and have it shipped for less than 8.00? Explain

1 answer

Let's first determine the cost of 1 ounce of paprika based on the given information.

  1. Cost of Paprika per 25 grams: The cost for 25 grams of paprika is $2.75.

    The cost per gram is: \[ \frac{2.75}{25} = 0.11 \text{ dollars/gram} \]

    To find the cost per ounce, we convert ounces to grams: \[ 1 \text{ ounce} = 28 \text{ grams} \]

    So, the cost per ounce is: \[ 28 \text{ grams} \times 0.11 \text{ dollars/gram} = 3.08 \text{ dollars/ounce} \]

  2. Cost of buying \( x \) ounces of paprika: The cost of buying \( x \) ounces is: \[ \text{Cost} = 3.08x \]

  3. Shipping Cost: The store charges 5% shipping on the purchase price, so the shipping cost is: \[ \text{Shipping Cost} = 0.05 \times (\text{Cost}) = 0.05(3.08x) \] Simplifying, we get: \[ \text{Shipping Cost} = 0.154x \]

  4. Total Cost: The total cost of buying \( x \) ounces of paprika, including shipping, is: \[ \text{Total Cost} = \text{Cost} + \text{Shipping Cost} = 3.08x + 0.154x \] Combining the terms: \[ \text{Total Cost} = (3.08 + 0.154)x = 3.234x \]

Now we can find the total cost when \( x = 2.5 \) ounces:

\[ \text{Total Cost} = 3.234 \times 2.5 \]

Calculating this gives: \[ \text{Total Cost} = 8.085 \]

So, the total cost of buying 2.5 ounces of paprika and shipping it would be $8.085.

Comparison with $8.00:

The total cost of $8.085 is more than $8.00.

Conclusion:

No, a customer cannot buy 2.5 ounces of paprika and have it shipped for less than $8.00. The total cost would be $8.085, which exceeds $8.00.