Question

isabel filled up her boat with 161.5 liters of fuel. she wants to know this amount of fuel in gallons. help isabel by completing the parts below. (a) let x be the unknown number of gallons. 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 3.8 161.5 (b) use the proportion from part (a) to find the amount of fuel in gallons. do not round any computations. gallons

Explanation:

Part (a)

Step1: Define Proportion Basis

We know the conversion: 1 gallon = 3.8 liters. So, the ratio of gallons to liters should be consistent. Let \( x \) be gallons for 161.5 liters. So, \(\frac{\text{gallons}}{\text{liters}}\) should be equal for both cases. Thus, \(\frac{x}{161.5}=\frac{1}{3.8}\) (or \(\frac{1}{3.8}=\frac{x}{161.5}\) as proportion can be set either way, but matching gallons over liters).

Step2: Fill the Proportion

Using the values \( x \), \( 1 \), \( 3.8 \), \( 161.5 \), the proportion is \(\frac{x}{161.5}=\frac{1}{3.8}\) (or \(\frac{1}{3.8}=\frac{x}{161.5}\), but arranging gallons (x, 1) over liters (161.5, 3.8)).

Step1: Cross - Multiply the Proportion

From \(\frac{x}{161.5}=\frac{1}{3.8}\), cross - multiply: \( 3.8x = 161.5\times1 \)

Step2: Solve for \( x \)

Divide both sides by 3.8: \( x=\frac{161.5}{3.8} \)
Calculate \(\frac{161.5}{3.8}\): \( 161.5\div3.8 = 42.5 \)

Answer:

(a):
\(\boldsymbol{\frac{x}{161.5} = \frac{1}{3.8}}\) (or \(\frac{1}{3.8}=\frac{x}{161.5}\), either correct as proportion)

Part (b)