The initial cost for attendance to carnival A is $12and each ride costs $2. The initial cost for attendance to carnival B is $16 and each ride cost $1.50.
a) in function notation write A(x) to represent the total cost of attending carnival A and going on x rides?
I did A(X)= 2x+12
b) in function notation write B(x) to represent the total cost of attending carnival B and going on x rides? I did B(x)=1.5x + 16
C) Determine the number of rides Jerry can go on such that the total cost of attending each carnival is the same.
2x+12=1.5x+16 2x=1.5x+4 .5x=4 x=8 so 8 rides
D) Jerry wants to go on 5 rides. Determine which carnival would be the lower total cost. justify your answer
a(X)=2(5)+12=$22 B(x)=1.5(5) +16 = $23.5
so Carnival A is cheaper for 5 rides
I think these are all correct but I just want to have them double checked. Thank you.
a. Correct.
b. Correct.
c. Correct.
d. Correct.
Thank you
Your answers are correct! Well done!
The functions A(x) = 2x + 12 and B(x) = 1.5x + 16 correctly represent the total cost of attending carnival A and B respectively, and going on x rides.
For determining the number of rides Jerry can go on such that the total cost of attending each carnival is the same, you correctly solved the equation 2x + 12 = 1.5x + 16 and found that x = 8 rides.
To determine which carnival would be the lower total cost for Jerry going on 5 rides, you correctly calculated A(5) = $22 for carnival A and B(5) = $23.5 for carnival B. Thus, carnival A would be the cheaper option.
Great job!
Your answers are correct! Well done. Here is a breakdown of each question and how you arrived at the correct answers:
a) To determine the total cost of attending carnival A and going on x rides, you correctly used the formula A(x) = 2x + 12. This is because the initial cost is $12, and for each ride, there is an additional cost of $2. So multiplying the number of rides by 2 and adding the initial cost gives you the total cost.
b) To determine the total cost of attending carnival B and going on x rides, you correctly used the formula B(x) = 1.5x + 16. This is because the initial cost is $16, and for each ride, there is an additional cost of $1.50. So multiplying the number of rides by 1.5 and adding the initial cost gives you the total cost.
c) To find the number of rides Jerry can go on such that the total cost of attending each carnival is the same, you correctly set the two equations equal to each other. 2x + 12 = 1.5x + 16. By solving this equation, you correctly found that x = 8. So Jerry can go on 8 rides.
d) To determine which carnival would have a lower total cost for 5 rides, you correctly calculated the total cost of attending carnival A and carnival B with 5 rides, using the respective formulas A(x) and B(x). You found that A(5) = $22 and B(5) = $23.50. Since A(5) is cheaper than B(5), you concluded that Carnival A would be the lower total cost option for 5 rides.
Overall, your answers are accurate and well-explained!