Question

an advertisement for a fish tank says the volume of the tank is 28 gallons. you want to know the volume of the tank in liters. find this by completing the parts below. (a) let x be the unknown number of liters. using the values below, create a proportion that can be used to find x. use the conversion 1 gallon = 3.8 liters. values: x, 1, 3.8, 28 (b) use the proportion from part (a) to find the volume of the tank in liters. do not round any computations.

Explanation:

Step1: Set up the proportion

We know that 1 gallon is equal to 3.8 liters. We want to find out how many liters (x) are in 28 gallons. So we set up the proportion: $\frac{1}{3.8}=\frac{28}{x}$? Wait, no, actually, the correct proportion is based on the ratio of gallons to liters. Since 1 gallon corresponds to 3.8 liters, then 28 gallons correspond to x liters. So the proportion should be $\frac{1}{3.8}=\frac{28}{x}$? Wait, no, let's think again. The ratio of gallons to liters should be consistent. So if 1 gallon is 3.8 liters, then the number of gallons over liters should be the same. So $\frac{\text{gallons}}{\text{liters}}=\frac{1}{3.8}=\frac{28}{x}$. Wait, no, actually, it's $\frac{\text{gallons}}{\text{liters}}$ for the first ratio (1 gallon to 3.8 liters) and then $\frac{28 \text{ gallons}}{x \text{ liters}}$. So the proportion is $\frac{1}{3.8}=\frac{28}{x}$. Wait, but maybe the other way: $\frac{\text{liters}}{\text{gallons}}=\frac{3.8}{1}=\frac{x}{28}$. Yes, that makes more sense. Because 3.8 liters per 1 gallon, so x liters per 28 gallons. So the proportion is $\frac{3.8}{1}=\frac{x}{28}$.

Step2: Solve for x

To solve for x, we can cross - multiply. Cross - multiplying gives us $1\times x = 3.8\times28$. So $x = 3.8\times28$. Let's calculate that. $3.8\times28=(4 - 0.2)\times28 = 4\times28-0.2\times28=112 - 5.6 = 106.4$. Wait, but the problem says not to round, but let's check the proportion again. Wait, the problem in part (a) is to set up the proportion, and part (b) is to use the proportion to find x. Wait, maybe I misread the problem. Wait, the problem says "create a proportion that can be used to find x". So the values given are x, 1, 3.8, 28. So the proportion is based on the conversion factor. So 1 gallon = 3.8 liters, so the ratio of gallons to liters is 1:3.8. Then for 28 gallons, the liters are x. So the proportion is $\frac{1}{3.8}=\frac{28}{x}$? No, that's not right. Wait, the correct proportion is $\frac{\text{gallons}}{\text{liters}}=\frac{1}{3.8}=\frac{28}{x}$? No, actually, it's $\frac{\text{liters}}{\text{gallons}}=\frac{3.8}{1}=\frac{x}{28}$. Yes, that's correct. Because 3.8 liters per 1 gallon, so x liters per 28 gallons. So the proportion is $\frac{3.8}{1}=\frac{x}{28}$.

Step3: Solve the proportion

To solve for x, we can multiply both sides of the equation $\frac{3.8}{1}=\frac{x}{28}$ by 28. So $x = 3.8\times28$. Calculating $3.8\times28$: $3\times28 = 84$, $0.8\times28=22.4$, so $84 + 22.4 = 106.4$.

Answer:

(a) The proportion is $\frac{3.8}{1}=\frac{x}{28}$ (or equivalent proportion like $\frac{1}{3.8}=\frac{28}{x}$ but the first one is more intuitive for liters per gallon). (b) The volume of the tank in liters is $106.4$.