Examkin

Question

Difficulty: MediumTranslating and Solving Algebraic Word Problems

A shipping company charges a flat fee of 1515 dollars plus 2.502.50 dollars per pound for the first 1010 pounds of a package's weight. For any weight exceeding 1010 pounds, the rate is 4.004.00 dollars per pound. If the total shipping charge for a package was 59.0059.00 dollars, what was the total weight of the package, in pounds?

  1. A
    11.011.0
  2. B
    11.611.6
  3. 14.7514.75Answer
  4. D
    17.617.6
  5. E
    18.518.5

Answer

The package's total weight was 14.75 pounds.
The correct answer of 14.75 pounds is found by setting up the equation representing the total shipping cost. First, calculate the cost for the first 10 pounds, which is the flat fee of 15.00 dollars plus 2.50 dollars per pound for 10 pounds: 15 + 2.50(10) = 40.00 dollars. Since the total charge of 59.00 dollars is greater than 40.00 dollars, the package must weigh more than 10 pounds. Let w be the total weight of the package. The remaining weight exceeding 10 pounds is w - 10, which is charged at 4.00 dollars per pound. Setting up the equation: 40 + 4(w - 10) = 59. Solving for w gives: 4(w - 10) = 19, which simplifies to w - 10 = 4.75, so w = 14.75.

Step-by-Step Solution

1
Calculate the cost for a package weighing exactly 10 pounds.
The cost is 15 + 2.50 * 10 = 40.00 dollars.
To determine whether the package exceeds 10 pounds by comparing it to the total charge of 59.00 dollars.
2
Set up an equation for the total cost where the weight w exceeds 10 pounds.
40 + 4.00 * (w - 10) = 59.00
To express the cost of the first 10 pounds plus the cost of the excess weight at 4.00 dollars per pound.
3
Solve the equation for the total weight w.
4 * (w - 10) = 19 -> w - 10 = 4.75 -> w = 14.75
To isolate and find the value of the variable representing the package weight.

Key Concept

Translating and Solving Algebraic Word Problems
Estimated Time:1m 30s
Rate this question

Topics

Translating and Solving Algebraic Word Problems

More questions from this topic