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
So a customer CAN NOT buy 2.5 ounces of paprika if you are being exact:
3.234(2.5) = 8.085
but it's really only .085 over budget.
the paprika costs .11 per gram ... 2.75/25
so 1 ounce costs 3.08 ... 28 * .11
buying and shipping x ounces
... (1 + .05) * 3.08 * x
cost = C
C = (2.75/25)(28/1)x + 0.05(2.75/25)(28/1)x
C = 3.234x
To determine the cost of buying and shipping x ounces of paprika, you need to follow these steps:
1. Convert the ounces into grams. Since 1 ounce is equal to 28 grams, multiply x by 28: 28 * x = 28x grams.
2. Calculate the cost of purchasing 28x grams of paprika. The spice store charges $2.75 for 25 grams, so the cost can be found by dividing 28x by 25 and multiplying it by $2.75: (28x / 25) * $2.75.
3. Calculate the shipping cost. The store charges 5% of the purchase price for shipping any order. To find the shipping cost, multiply the purchase price by 5% (or 0.05): (28x / 25) * $2.75 * 0.05 = (28x * $0.11) / 25 = $0.11x.
4. Add the purchase price and shipping cost to get the total cost: (28x / 25) * $2.75 + $0.11x.
Now, to determine whether a customer can buy 2.5 ounces of paprika and have it shipped for less than $8.00, you can substitute x with 2.5 and evaluate the expression:
(28 * 2.5 / 25) * $2.75 + $0.11 * 2.5 = $5.60.
Since $5.60 is less than $8.00, a customer can indeed buy 2.5 ounces of paprika and have it shipped for less than $8.00.