Question

suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. when carrying 10 gallons of fuel, the airplane weighs 2058 pounds. when carrying 35 gallons of fuel, it weighs 2203 pounds. how much does the airplane weigh if it is carrying 55 gallons of fuel?

pounds

Explanation:

Step1: Find the slope (rate of change)

The weight \( y \) is a linear function of fuel \( x \), so \( y = mx + b \). We have two points: \((10, 2058)\) and \((35, 2203)\). The slope \( m \) is \(\frac{2203 - 2058}{35 - 10}=\frac{145}{25} = 5.8\) pounds per gallon.

Step2: Find the y-intercept \( b \)

Using the point \((10, 2058)\) and \( m = 5.8 \) in \( y = mx + b \): \( 2058 = 5.8\times10 + b \). So \( 2058 = 58 + b \), then \( b = 2058 - 58 = 2000 \). The equation is \( y = 5.8x + 2000 \).

Step3: Calculate weight at 55 gallons

Substitute \( x = 55 \) into \( y = 5.8x + 2000 \): \( y = 5.8\times55 + 2000 \). First, \( 5.8\times55 = 319 \). Then \( y = 319 + 2000 = 2319 \).

Answer:

2319