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Question

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Decreasing fuel consumption is important to the airline industry. Engineers estimate that a 1 percent reduction in weight corresponds to a 0.75 percent reduction in fuel costs. Now, imagine that a certain plane weighs 129,520 pounds. The next generation of this plane weighs 126,606 pounds. Estimate the percent reduction in fuel costs from one generation to the next. Express your answer to the nearest hundredth percent.
Hint
1.96 percent
1.66 percent
1.69 percent
1.99 percent

Answer 1

Hi Tori,

 

Let's begin by calculating the percent difference for the weight change of the plane from the 1st generation to the 2nd generation:

    F = first generation weight

    S = second generation weight

    P = percent weight change

    P = [(F - S)/F] x 100%

    P = [(129,520 - 126,606)]/129,520 x 100%

    P = 2,914/129,520 x 100%

    P = 0.02249845584 x 100%

    P = 2.25% (rounded to nearest hundredth)

 

Next, we can set up this proportion and then plug in our known values to solve for our unknown:

    W₁ : F₁ = W₂ : F₂  [proportion] 

        W₁ = given percent weight reduction

         F₁ = given percent fuel cost reduction

        W₂ = calculated percent weight reduction

         F₂ = unknown percent fuel cost reduction

 

    1 : 0.75 = 2.25 : F₂  [known values & unknown]

    1/0.75 = 2.25/F₂

    (1)(F₂) = (0.75)(2.25)

    F₂ = 1.6875

    F₂ = 1.69% (rounded to nearest hundredth)

 

The concept of a proportion was key to solving this problem.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan.