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 20 gallons of fuel, the airplane weighs 2130 pounds. When carrying 48 gallons of fuel, it weighs 2312 pounds. How much does the airplane weighs if it is carrying 64 gallons of fuel?

Answer 1

Weight of Airplane will be 2416 pounds when it is carrying 64 gallons of fuel.

Explanation:

Given:

20 gallons of fuel, the airplane weighs 2130 pounds

48 gallons of fuel, it weighs 2312 pounds

so we can say that we have 2 points of value.

Let the number of gallons of fuel be 'x'.

Eight of the airplane be denoted by 'y'.

So we can say that;

`(x_1,y_1)=(20,2130)`

`(x_2,y_2)=(48,2312)`

Now we know that;

weight (in pounds) of an airplane is a linear function of the amount of fuel ( in gallons) in its tank.

So we can say that;

`y=mx+b`

where m⇒ slope

b⇒ intercept.

first we will find the slope:

`m= (y_2-y_1)/(x_2-x_1) = (2312-2130)/(48-20)=(182)/(28)=6.5`

Now we will find the intercept by substituting the values;

`y=6.5x+b\\\\2130=6.5* 20+b\\\\2130 = 130+b\\\\b=2130-130 = 2000`

so we get the equation as;

`y =6.5x+2000`

Now we need to find airplane weighs
`(y)` if it is carrying 64 gallons of fuel(
`(x=64).`

`y=6.5* 64 +2000\\\\y=2416\ pounds`

Hence Weight of Airplane will be 2416 pounds when it is carrying 64 gallons of fuel.