2009 AMC 12B Question 8 - thichhoctoan.com

Question 8

When a bucket is two-thirds full of water, the bucket and water weigh $a$ kilograms. When the bucket is one-half full of water the total weight is $b$ kilograms. In terms of $a$ and $b,$ what is the total weight in kilograms when the bucket is full of water?

$\dfrac{2}{3}a + \dfrac{1}{3}b$
$\dfrac{3}{2}a - \dfrac{1}{2}b$
$\dfrac{3}{2}a + b$
$\dfrac{3}{2}a + 2b$
$3a - 2b$