a tool rental company charges $25 for the first hour of a tractor rental. each additional hour costs $20 per…

a tool rental company charges $25 for the first hour of a tractor rental. each additional hour costs $20 per hour. which statement describes the relationship between total cost and hours? \n- it is proportional; each ratio \\(\\frac{y}{x}\\) for related pairs is equivalent. \n- it is proportional; each x - term is a multiple the previous term. \n- it is not proportional; each ratio \\(\\frac{y}{x}\\) for related pairs is not equivalent. \n- it is not proportional; each x - term is not a multiple the previous term.

a tool rental company charges $25 for the first hour of a tractor rental. each additional hour costs $20 per hour. which statement describes the relationship between total cost and hours? \n- it is proportional; each ratio \\(\\frac{y}{x}\\) for related pairs is equivalent. \n- it is proportional; each x - term is a multiple the previous term. \n- it is not proportional; each ratio \\(\\frac{y}{x}\\) for related pairs is not equivalent. \n- it is not proportional; each x - term is not a multiple the previous term.

Answer

Explanation:

Step1: Recall proportional relationship

A proportional relationship has a constant ratio $\frac{y}{x}$ (where $y$ is total cost, $x$ is hours) and passes through the origin.

Step2: Analyze the cost function

For $x = 1$ hour, cost $y = 25$. For $x = 2$ hours, cost $y = 25 + 20 = 45$. For $x = 3$ hours, cost $y = 25 + 20\times2 = 65$.

Step3: Calculate ratios $\frac{y}{x}$

  • For $x = 1, y = 25$: $\frac{25}{1} = 25$
  • For $x = 2, y = 45$: $\frac{45}{2} = 22.5$
  • For $x = 3, y = 65$: $\frac{65}{3}\approx21.67$ These ratios are not equal, so the relationship is not proportional, and the reason is the ratios $\frac{y}{x}$ are not equivalent.

Answer:

It is not proportional; each ratio $\frac{y}{x}$ for related pairs is not equivalent.