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Zorluk: OrtaSystems of Linear Equations

An online retailer offers two shipping options for heavy packages. The first option charges a flat fee of 15.0015.00 dollars plus 1.501.50 dollars per pound of the package's weight. The second option charges a flat fee of 27.0027.00 dollars plus 0.700.70 dollars per pound of the package's weight. If a package of weight ww pounds costs the same total amount of cc dollars under both options, what is the value of ww?

  1. A
    1.5
  2. B
    37.5
  3. C
    52.5
  4. 15Cevap

Cevap

15
To find the weight of the package that yields the same cost under both shipping options, we set the cost expressions equal to each other. The first option is represented by c=1.50w+15c = 1.50w + 15 and the second by c=0.70w+27c = 0.70w + 27. Setting them equal gives 1.50w+15=0.70w+271.50w + 15 = 0.70w + 27. Subtracting 0.70w0.70w from both sides results in 0.80w+15=270.80w + 15 = 27. Subtracting 1515 from both sides gives 0.80w=120.80w = 12. Dividing by 0.800.80 yields w=15w = 15. Therefore, the weight of the package is 15 pounds.

Adım Adım Çözüm

1
Set up the linear equations representing the total cost c for each shipping option based on the package's weight w.
The first option is represented by c=1.50w+15c = 1.50w + 15, and the second option is represented by c=0.70w+27c = 0.70w + 27.
This models the real-world scenario into a system of two linear equations with two variables.
2
Set the two expressions for the total cost c equal to each other to solve for the weight w.
1.50w+15=0.70w+271.50w + 15 = 0.70w + 27
Since the package costs the same under both options, the cost values are equal at this specific weight.
3
Isolate the variable w by subtracting 0.70w0.70w and 1515 from both sides of the equation.
0.80w=120.80w = 12, which simplifies to w=15w = 15.
Subtracting 0.70w0.70w from both sides isolates the variable terms on the left, and subtracting 1515 isolates the constants on the right. Dividing by 0.800.80 solves for w.

Anahtar Kavram

Solving a system of linear equations by setting the expressions equal to find the point where two rates intersect.
Tahmini Süre:1m 30s
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Systems of Linear Equations

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