Study Notes on Toy Car Weight Problem and Sum Evaluation

Problem 1: Weight of Toy Cars

• Total Weight of Toy Cars: 3.85 lbs
• Weight of Heaviest Car: 1 lb
• Weight of Other Cars:
    - Let the weight of each of the other three cars be denoted as $x$.
    - Since the total weight is given by the equation:
  $1 + 3x = 3.85$
    - Rearranging gives:
  $3x = 3.85 - 1$
  $3x = 2.85$
  $x = \frac{2.85}{3}$
  $x = 0.95$ lbs
• Comparison of Weights:
    - The heaviest car weighs 1 lb and each of the other cars weighs 0.95 lbs.
• Calculation of Difference in Weight:
    - To find how much more the heaviest car weighs than one of the other cars:
  $1 - 0.95 = 0.05$ lbs
• Final Answer: The heaviest car weighs 0.05 lbs more than each of the other cars.

Problem 2: Sum Evaluation

• Sum Given: $ext{Evaluate the sum } ext{S} = extstyle \bigg( extstyle ext{Σ (5k + 8)}$
• Limits of Summation: from $k = 1$ to some maximum value.
• Calculating the Sum for a Specific Range:
    - (Assuming we evaluate for $k = 1$ to $k = n$ where n is specified, if unspecified let us use 2 for example)
• For $n = 2$, we calculate the sum:
    - When $k = 1$,
  $5(1) + 8 = 13$
    - When $k = 2$,
  $5(2) + 8 = 18$
• Total Sum:
    - $S = 13 + 18 = 31$
• Final Answer for Sum Evaluation: Total sum from $k = 1$ to $k = 2$ is 31.