Problema Solution
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
20
gallons of fuel, the airplane weighs
2130
pounds. When carrying
54
gallons of fuel, it weighs
2351
pounds. How much does the airplane weigh if it is carrying
62
gallons of fuel?
Answer provided by our tutors
the weight (in pounds) 'y' of an airplane is a linear function of the amount of fuel (in gallons) 'x' in its tank means:
y = a*x + b, where a and b are constants
when carrying 20 gallons of fuel, the airplane weighs 2130 pounds:
x = 20 gal
y = 2130 lbs
2130 = 20a + b
when carrying 54 gallons of fuel, it weighs 2351 pounds:
x = 54 gal
y = 2351 lbs
2351 = 54a + b
by solving the system of equations:
20a + b = 2130
54a + b = 2351
we find:
a = 6.5
b = 2000
click here to see the step by step solution of the system of equations:
y = 6.5x + 2000 is the linear equation
x = 62 gal
y = 6.5*62 + 2000
y = 2403 lbs
the weight of the airplane that is carrying 62 gallons of fuel is 2403 pounds.