Question

1. construct arguments a regular tube of toothpaste costs $2.50 for 3.2 ounces. a travel size tube costs $1.00 for 1.2 ounces. compare the prices and weights using percent to decide which is the better buy.

Explanation:

Step1: Find unit price of regular tube

Unit price = Total cost / Total ounces. For regular tube: $\frac{2.50}{3.2} \approx 0.78125$ dollars per ounce.

Step2: Find unit price of travel tube

For travel tube: $\frac{1.00}{1.2} \approx 0.8333$ dollars per ounce.

Step3: Calculate percentage difference in unit price

Let regular tube's unit price be $P_r \approx 0.78125$, travel tube's $P_t \approx 0.8333$. The percentage by which travel tube's unit price is higher than regular: $\frac{P_t - P_r}{P_r} \times 100 = \frac{0.8333 - 0.78125}{0.78125} \times 100 \approx 6.67\%$. Or, percentage of travel tube's unit price relative to regular: $\frac{P_t}{P_r} \times 100 \approx \frac{0.8333}{0.78125} \times 100 \approx 106.67\%$, meaning travel tube costs ~6.67% more per ounce. Also, check weight: regular has 3.2 oz, travel has 1.2 oz. The percentage of travel's weight to regular: $\frac{1.2}{3.2} \times 100 = 37.5\%$. So for 37.5% of the regular's weight, travel costs 100% of regular's cost (since travel is $1, regular's 37.5% weight would be 3.2*0.375 = 1.2 oz, and regular's cost for 1.2 oz is 2.50*0.375 = 0.9375$). So travel costs $1 for 1.2 oz, regular would cost ~$0.9375 for 1.2 oz. The percentage by which travel's cost is higher for same weight: $\frac{1 - 0.9375}{0.9375} \times 100 \approx 6.67\%$. Thus, regular tube is better buy as it costs less per ounce (or for same weight, travel is ~6.67% more expensive).

Answer:

The regular tube of toothpaste is the better buy. The travel - size tube's unit price (cost per ounce) is approximately 6.67% higher than the regular tube's unit price, and the travel - size tube's weight is only 37.5% of the regular tube's weight while its cost for the same weight (1.2 ounces) is about 6.67% higher than the regular tube's cost for that weight.