Question

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?

$\dfrac{1}{12}$

$\dfrac{1}{6}$

$\dfrac{1}{4}$

$\dfrac{1}{3}$

$\dfrac{1}{2}$

Answer: B

Concepts:ratio and proportion fraction

Difficulty rating: 1020

Small Hint:

Write Mia, Sofia, Pablo as $m,2m,6m$

Big Hint:

Equal sharing means each person ends with $3m$ eggs

Solution:

Let $m$ be the number of candy eggs that Mia had. Then Sofia had $2m$ eggs and Pablo had $6m$ eggs.

The total number of eggs is then $m + 2m + 6m = 9m.$ For all of them to have the same number of eggs, they each must have $9m \div 3 = 3m$ eggs.

Sofia needs $3m - 2m = m$ more eggs. This means Pablo must give $\dfrac{m}{6m} = \dfrac{1}{6}$ of his eggs to Sofia.

Thus, B is the correct answer.

2015 AMC 10A Problem 4

Answer: B

Difficulty rating: 1020

Small Hint:

Big Hint:

Solution:

Problem 4 in Other Years