Final answer:
The ratio of casts to caught fish for James should be represented as F = P/8, not F = 8P. Based on the correct relationship, if James caught 32 fish, he cast his pole 256 times, and when he cast his pole 64 times, he indeed caught 8 fish.
Step-by-step explanation:
The student's question involves understanding ratios and using them to make calculations related to James's fishing trip. If the ratio of the number of times James cast his fishing pole, P, to the number of times he caught a fish, F, was 8:1, this means that for every 8 times James cast his pole, he caught 1 fish. Therefore, the equation to determine the number of fish caught based on the number of casts would be F = P/8, not F = 8P as stated in the question. To use this equation in practice:
Correcting the Equation
For example, if James caught 32 fish, then using the correct equation, he would have cast his pole 32 x 8 = 256 times, not 4 times.
Using the Correct Equation
If James cast his fishing pole 64 times, then the number of fish he caught can be calculated using the correct equation: 64 / 8 = 8 fish. So this statement is true.
When it comes to predicting average numbers based on ratios, it's important to use the correct mathematical relationship, which was not F = 8P as initially described.