Mrs Olive gave her 4 children a sack of candy to share. Mark ate 1/2 of the candy in the sack and passed the sack to Rachel. Rachel ate 1/3 of the remaining candy and passed the sack to Fred. Fred then ate 1/4 of the candy that remained and passed the sack to Britany. Britany ate the last 12 pieces of candy. How many pieces of candy did Mark eat?
original amount = x
mark ate x/2, leaving x/2
Rachel ate 1/3(x/2) = x/6, leaving x/3
Fred ate 1/4(x/3) = x/12, leaving x/4
Britany ate 12 = x/4
so, x=48
check
Mark ate 24, left 24
Rachel ate 8, left 16
Fred ate 4, left 12
Britany: 12
To solve this problem, we need to break it down step by step. Let's go through the scenario:
Step 1:
Mark ate 1/2 of the candies in the sack. So, we can calculate the candies left after Mark ate as 1 - 1/2 = 1/2.
Step 2:
Rachel ate 1/3 of the remaining candies. Since there were 1/2 left after Mark, we can calculate Rachel's share as 1/2 * 1/3 = 1/6. Thus, there were 1/2 - 1/6 = 1/3 of the candies remaining after Rachel.
Step 3:
Fred ate 1/4 of the remaining candies. So, we can calculate Fred's share as 1/3 * 1/4 = 1/12. Therefore, there were 1/3 - 1/12 = 1/4 of the candies remaining after Fred.
Step 4:
Britany ate the last 12 pieces of candy. Since we know that 1/4 of the candies were left, we can use the equation 1/4 = 12 to find the original number of candies.
To solve for the total number of candies, we multiply both sides of the equation by 4, giving us 1 = 12 * 4 = 48 candies.
Finally, to find out how many candies Mark ate, we take the initial number (48) and subtract the remaining candies after Britany (12): 48 - 12 = 36.
Therefore, Mark ate 36 pieces of candy.