Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides
to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs. What fraction of his eggs should Pablo give to Sofia?
i dont care
To solve this problem, let's go step by step:
1. Let's assume that Mia has x candy eggs.
2. It is given that Sofia has twice as many eggs as Mia. So, Sofia has 2x candy eggs.
3. It is also given that Pablo has three times as many eggs as Sofia. So, Pablo has 3 * 2x = 6x candy eggs.
Now, we need to find how many eggs Pablo needs to give to Sofia (S) and Mia (M) in order for all three to have an equal number of eggs.
Let's say he gives y eggs to both Sofia and Mia:
- Before sharing: Sofia has 2x candy eggs, Mia has x candy eggs, and Pablo has 6x candy eggs.
- After sharing: Sofia will have 2x + y candy eggs, Mia will have x + y candy eggs, and Pablo will have 6x - 2y candy eggs.
To make it equal, we need to equate the number of eggs after sharing:
2x + y = x + y = 6x - 2y
Simplifying the equation, we get:
2x + y = 6x - 2y
3x = 3y
x = y
Thus, we can conclude that Pablo needs to give an equal number of eggs to both Sofia and Mia. Since Sofia initially has 2x candy eggs and he needs to give away x eggs, he should give away x/2 eggs to Sofia.
So, the fraction of his eggs that Pablo should give to Sofia is x/2x = 1/2.
Therefore, Pablo should give 1/2 of his eggs to Sofia.
p=3s
s=2m
p-(x+y) = s+x
p-(x+y) = m+y
If p gives away 1/2 of his eggs,
1/6 to s and 1/3 to m, then
Pablo has p/2
Sofia has p/3 + p/6 = p/2
Mia has p/6 + p/3 = p/2