Final answer:
Using algebra, we determine Nate received 24 pieces of candy, Ben received 16 pieces, and Anne received 32 pieces, based on the given relationships and the total of 72 pieces.
Step-by-step explanation:
Nate, Ben, and Anne went trick or treating, and we need to find out how many pieces of candy each person received. We are given that all together, they got 72 pieces of candy. Let's denote the amount of candy that Nate got as N. According to the problem, Ben received 8 fewer pieces than Nate, so Ben got N - 8 pieces. Anne got twice as many pieces of candy as Ben, so Anne got 2(N - 8) pieces.
Now, we can create an equation based on the total candy they collected together:
N + (N - 8) + 2(N - 8) = 72
Simplifying this, we get
4N - 24 = 72
Adding 24 to both sides gives us
4N = 96
Dividing both sides by 4 gives us
N = 24
Now we can use N to find out how much candy Ben and Anne got:
Ben: N - 8 = 24 - 8 = 16
Anne: 2(N - 8) = 2(24 - 8) = 2(16) = 32
Nate received 24 pieces, Ben received 16 pieces, and Anne received 32 pieces of candy.