Final answer:
The correct equation to represent the number of puzzle pieces placed over time would be p = 540t, based on 12,971 pieces being placed over 24 hours at a constant rate. However, none of the options presented in the question are correct; the closest incorrect option given the rounding applied is d) 12,971 = 540t + 12971.
Step-by-step explanation:
We are given that the Spanish team placed 12,971 pieces in 24 hours. If we assume that they were placing pieces at a constant rate, we want to relate the number of pieces placed (p) with the time (t) in hours. We can start by dividing the total number of pieces by the total time to get the rate of pieces placed per hour. The rate will be 12,971 pieces divided by 24 hours, which gives us approximately 540.46 pieces per hour.
Since we're looking at pieces placed (p) as a function of time (t), and the rate of placement is constant, we can express p as the product of the rate and time. Our equation should thus be p = rate × t. With the given numbers, our rate is 540.46, so the equation becomes:
p = 540.46 × t
However, the options provided seem to have rounded this number to 540, so the closest matching equation from the choices given would be:
p = 540 × t
This particular equation helps us predict the number of 12971 pieces that would be placed given any number of hours. Therefore, the correct answer is not explicitly given in the options, but the best representation considering the rounding used would be none of the choices as they do not correctly represent the relationship between time and the number of pieces placed in the correct format, as they include extraneous terms or omit the variable p altogether. However, if we were to choose the closest incorrect option, it would be:
d) 12,971 = 540t + 12971, which is the only one that contains the correct rate of 540 pieces per hour. This is still an incorrect equation because it improperly adds 12,971 to the product of 540 and t, but none of the given options is exactly correct.