To determine the original number of peanuts, we can work our way backwards from the remaining quantity of 71 peanuts.
Let's break down the process step by step:
1. Phillip took 1/3 of the peanuts. So, after Phillip took his share, the remaining peanuts would be (2/3) of the original amount.
2. Joy took 1/4 of the remaining peanuts, which means she took (1/4) * (2/3) = 2/12 = 1/6 of the original quantity.
3. After Joy took her share, the remaining peanuts would be (1 - 1/6) = 5/6 of the original amount.
4. Brent took 1/2 of the remaining peanuts, which is (1/2) * (5/6) = 5/12 of the original quantity.
5. Finally, after Brent took his share, the remaining peanuts would be (1 - 5/12) = 7/12 of the original amount, which is equal to 71 peanuts.
Now, let's calculate the original number of peanuts:
(7/12) * (original quantity) = 71
To isolate the original quantity, multiply both sides of the equation by (12/7):
(original quantity) = 71 * (12/7)
(original quantity) = 122.57
Since we can't have a fraction or a decimal number of peanuts, we can conclude that the original number of peanuts must have been 122.