Question 1195183: Suppose that the weight (in pounds) of an airplane is a linear function of the total amount of fuel (in qallons) in its tank. When graphed, the function gives a line
with a slope of 5.5. See the figure below.
With 47 gallons of fuel in its tank, the airplane has a weight of 2258.5 pounds. What is the weight of the plane with 13 gallons of fuel in its tank?
2258.5
Airplane
weight
(in pounds)
pounds
×
S
P
Amount of fuel
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! linear equation is y = mx + b
m is the slope
b is the y-intercept
x is the number of gallons of fuel in the tank.
y is the weight of the airplane.
with a slope of 5.5, the equation becomes:
y = 5.5 * x + b
when x = 47, y = 2258.5
equation becomes:
2258.5 = 5.5 * 47 + b
solve for b to get:
b = 2258.5 - 5.5 * 47 = 2000.
the equation becomes:
y = 5.5 * x + 2000
2000 is the weight of the plane with no fuel in it.
when x = 47, the equation becomes:
y = 5.5 * 47 + 2000 = 2258.5.
this was the weight of the plane given in the statement of the problem, which confirms the equation is good.
with 13 gallons of fuel in it, the equation becomes:
y = 5.5 * 13 + 2000 = 2071.5
that's your solution.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The weight is a linear function of the amount of fuel; the slope of 5.5 means each gallon of fuel adds 5.5 pounds to the weight.
The difference between 47 gallons and 13 gallons is 34 gallons; at 5.5 pounds per gallon, that is 34(5.5) = 187 pounds.
The weight with 47 gallons of fuel is 2258.5 pounds, so the weight with 13 gallons of fuel is 2258.5-187 = 2071.5.
ANSWER: 2071.5 pounds
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