Question

Use the tables to answer the question.

Sweet Sugar
Weight (lbs.) Price ($)
2.5 0.75
15.0 4.50
30.0 9.00
100.0 30.00
 
Super Sugar
Weight (lbs.) 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, Suman determined that Sweet Sugar was the better buy based on price alone. How much money per pound will Suman save if he buys the Sweet Sugar brand?

Answer 1

To determine how much Suman will save per pound by buying Sweet Sugar instead of Super Sugar, we need to calculate the price per pound for both brands.

**Sweet Sugar:**
- Price ($) / Weight (lbs.)
1. For 2.5 lbs: \( \frac{0.75}{2.5} = 0.30 \) $/lb
2. For 15.0 lbs: \( \frac{4.50}{15.0} = 0.30 \) $/lb
3. For 30.0 lbs: \( \frac{9.00}{30.0} = 0.30 \) $/lb
4. For 100.0 lbs: \( \frac{30.00}{100.0} = 0.30 \) $/lb

The price per pound for Sweet Sugar is consistently **$0.30**.

**Super Sugar:**
- Price ($) / Weight (lbs.)
1. For 3.75 lbs: \( \frac{1.16}{3.75} \approx 0.3093 \) $/lb
2. For 10.0 lbs: \( \frac{3.10}{10.0} = 0.31 \) $/lb
3. For 25.0 lbs: \( \frac{7.75}{25.0} = 0.31 \) $/lb
4. For 110.0 lbs: \( \frac{34.10}{110.0} \approx 0.3100 \) $/lb

The price per pound for Super Sugar is approximately **$0.31**.

Now we can calculate how much money per pound Suman will save by buying Sweet Sugar instead of Super Sugar:

\[
\text{Savings} = \text{Price per pound of Super Sugar} - \text{Price per pound of Sweet Sugar} = 0.31 - 0.30 = 0.01 \text{ $/lb}
\]

Thus, Suman will save **$0.01 per pound** by choosing Sweet Sugar over Super Sugar.