The smaller of the two containers has a capacity of 150 gallons. When it is $\frac{4}{5}$ full, its contents are emptied into a larger container, filling exactly $\frac{2}{3}$ of it. What is the capacity, in gallons of the larger container?
The capacity of the larger container is 270 gallons.
If the larger container holds 270 gallons, then when it's 2/3 full it would contain 180 gallons.
This is more than the entire capacity of the smaller container.
When the smaller container is 4/5 full, it is holding 120 gallons ...... 4/5 x 150 = 120
120 is 2/3 of 180 gallons ...... so the capacity of the larger container is 180 gallons.
.
