Cameron put his dog Buddy in a kennel while he went on a long business trip. The equation [tex]$y=15 x+25$[/tex] shows the total charge [tex]$y$[/tex] that Cameron will pay to put Buddy in a kennel for [tex]$x$[/tex] days. Which statement is true?
A. The kennel charges $25 per day with an initial fee of $15.
B. The kennel charges an initial fee of $25 and $15 per day.
C. The kennel charges $25 for the first day and $15 per day after the first day.
D. The kennel charges $15 for the first day and $25 per day after the first day.
Answer (1)
The equation y = 15 x + 25 represents the total cost of keeping a dog in a kennel. The coefficient of x , which is 15, represents the cost per day, and the constant term, 25, represents the initial fee. Therefore, the kennel charges an initial fee of $25 and $15 per day. The final answer is: The kennel charges an initial fee of $25 and $15 per day.
Explanation
Understanding the Equation The equation given is y = 15 x + 25 , where y is the total charge and x is the number of days Buddy stays in the kennel. We need to interpret what the numbers 15 and 25 represent in this equation.
Identifying the Cost per Day and Initial Fee In the equation y = 15 x + 25 , the number 15 is multiplied by x , which represents the number of days. This means that 15 is the cost per day. The number 25 is a constant term, which means it is a fixed cost regardless of the number of days. This is the initial fee.
Selecting the Correct Statement Therefore, the kennel charges an initial fee of $25 and $15 per day. Comparing this with the given statements, the correct statement is: The kennel charges an initial fee of $25 and $15 per day.
Examples
Understanding linear equations like y = 15 x + 25 helps in everyday budgeting. For instance, if you're planning a road trip and know you'll spend $25 on gas and 15 p er d a yo n f oo d , t hi se q u a t i o nh e lp syo u c a l c u l a t eyo u r t o t a l e x p e n ses . I f t h e t r i pl a s t s 3 d a ys , t h e t o t a l cos tw o u l d b e y = 15 \times 3 + 25 = $70. This kind of calculation is useful for managing personal finances and making informed decisions about costs.
