Bunuel wrote:

At the start of the day the amount of water in two identical buckets is 3 liters in bucket A and 2 liters in bucket B. If x liters are then added to A and 4x liters are added to B so that the ratio of A to B is 3 to 10, how much water has been added to bucket B?

A. 4 liter

B. 12 liters

C 16 liters

D. 48 liters

E. 72 liters

This question changes what we normally see, but solving it is done similarly.

Usually there is a given original ratio with a multiplier and quantities to be added or subtracted that yield a new ratio.

Neither ratio here "takes" the multiplier. Instead, in the arithmetic, the multiplier accompanies the amounts added.

Original ratio: \(\frac{A}{B} =

\frac{3}{2}\)

Add x liters to A and 4x liters to B, to yield a new ratio

\(\frac{3 + x}{2 +

4x}=\frac{3}{10}\)

\(3(2 + 4x) = 10(3 + x)\)

\(6 + 12x = 30 + 10x\)

\(2x = 24\)

\(x = 12\)

How much water was added to B?

This time the multiplier corresponds with amounts added.

B got 4x liters of water

x = 12

4x = 48 liters

Answer D