Subjects algebra

Unit Price Comparison

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** We need to compare prices of various products purchased in Canada and the US by calculating unit prices in consistent units (mL or sheets) and converting US prices to Canadian dollars (CAD) to determine the best buy. 2. **Formula for unit price:** - For liquids: Unit price per mL = $\frac{\text{Price}}{\text{Volume in mL}}$ - For solids (weight to volume conversion needed): Plan to convert kg or g to mL using density (mass/volume) if known. - For sheets (bathroom tissue): Unit price per sheet = $\frac{\text{Price}}{\text{Number of sheets}}$ 3. **Important rules:** - Convert all prices to the same currency (CAD) using the current exchange rate (not provided, so assume a rate or state it as a variable). - Convert weights to volumes for solids if density is known or estimate. - For powdered tea mix and peanut butter, explain conversion plans without calculations. 4. **Calculate Canadian unit prices:** - Johnson's Baby Shampoo: $\frac{4.97}{592} \approx 0.00839$ CAD/mL - Arm & Hammer Liquid Laundry Detergent: $\frac{12.97}{6210} \approx 0.00209$ CAD/mL - Lipton Powdered Tea Mix: Conversion needed from kg to mL (density required). - Heinz Tomato Ketchup: $\frac{5.97}{750} = 0.00796$ CAD/mL - Peanut Butter: Conversion needed from g to mL (density required). - Bathroom Tissue: $\frac{14.97}{24 \times 253} = \frac{14.97}{6072} \approx 0.00247$ CAD/sheet 5. **Calculate American unit prices:** - Johnson's Baby Shampoo: $\frac{6.49}{443.6} \approx 0.01463$ USD/mL - Arm & Hammer Liquid Laundry Detergent: $\frac{6.15}{1478.7} \approx 0.00416$ USD/mL - Lipton Powdered Tea Mix: Conversion needed. - Heinz Tomato Ketchup: $\frac{3.19}{384.5} \approx 0.00830$ USD/mL - Peanut Butter: $\frac{4.09}{473.2} \approx 0.00864$ USD/mL - Bathroom Tissue: $\frac{5.49}{4 \times 1000} = \frac{5.49}{4000} = 0.00137$ USD/sheet 6. **Conversion to CAD:** - To compare, multiply American unit prices by exchange rate $r$ (USD to CAD). For example, American unit price in CAD = American unit price in USD $\times r$. 7. **Plans for conversions:** - Powdered Tea Mix: To convert kg to mL, need density (g/mL). Then $\text{Volume} = \frac{\text{Mass}}{\text{Density}}$. - Peanut Butter: Similarly, convert g to mL using density. 8. **Best buy determination:** - After converting all prices to CAD per consistent unit, compare values. - The product with the lowest unit price in CAD is the best buy. **Summary:** - Calculate unit prices in consistent units. - Convert US prices to CAD using exchange rate. - Convert weights to volumes using density for solids. - Compare unit prices to find best buy. This method ensures fair comparison across different units and currencies.