Question

Sweet sugar
Weight. Price
2.5. 0.75
15.0. 4.50
30.0. 9.00
100.0. 30.00

Super sugar
Weight. Price
3.75. 1.16
10.0. 3.10
25.0. 7.75
110.0. 34.10
Based on the tables showing the price of buying different amounts of two brands of sugar, human determined that sweet sugar was the better buy based on price alone. How much money per pound will Shuman save if he buys the Sweet sugar brand?

Answer 1

To determine how much money per pound Shuman will save by buying the Sweet Sugar brand instead of the Super Sugar brand, we first need to calculate the price per pound for each brand.

**Sweet Sugar:**

1. For 2.5 lbs:
\[
\text{Price per pound} = \frac{0.75}{2.5} = 0.30 \text{ dollars per pound}
\]

2. For 15.0 lbs:
\[
\text{Price per pound} = \frac{4.50}{15.0} = 0.30 \text{ dollars per pound}
\]

3. For 30.0 lbs:
\[
\text{Price per pound} = \frac{9.00}{30.0} = 0.30 \text{ dollars per pound}
\]

4. For 100.0 lbs:
\[
\text{Price per pound} = \frac{30.00}{100.0} = 0.30 \text{ dollars per pound}
\]

**Super Sugar:**

1. For 3.75 lbs:
\[
\text{Price per pound} = \frac{1.16}{3.75} \approx 0.3093 \text{ dollars per pound}
\]

2. For 10.0 lbs:
\[
\text{Price per pound} = \frac{3.10}{10.0} = 0.31 \text{ dollars per pound}
\]

3. For 25.0 lbs:
\[
\text{Price per pound} = \frac{7.75}{25.0} = 0.31 \text{ dollars per pound}
\]

4. For 110.0 lbs:
\[
\text{Price per pound} = \frac{34.10}{110.0} \approx 0.3100 \text{ dollars per pound}
\]

**Comparison:**

- **Sweet Sugar price per pound:** \(0.30\) dollars
- **Super Sugar price per pound:** approximately \(0.3093\) to \(0.31\) dollars

**Savings Calculation:**

\[
\text{Savings per pound} = \text{Price of Super Sugar} - \text{Price of Sweet Sugar}
\]

Using the higher estimated price for Super Sugar (i.e., 0.31):

\[
\text{Savings} = 0.31 - 0.30 = 0.01 \text{ dollars per pound}
\]

Thus, Shuman will save approximately **1 cent per pound** if he buys the Sweet Sugar brand.