SAT Math prune drying percentages problem

Question

I encountered this SAT type Math question and do not know how to progress.

Before a plum is dried to become a prune, it is 92% water. A prune is just 20% water. If only water is evaporated in the drying process, how many pounds of prunes can be made with 100 pounds of plums?

My attempt:

Since a prune is just 20% water and a plum is 92% water (before it is dried), we want the 8% of other to become 80%. Now here, I am not sure what to do next. Any help would be appreciated. Thanks!

Answer 1

There is 8 lb of dry matter in the plums. This is $80\%$ of the weight of the prunes, so the weight of the prunes is $\frac 8{0.8}=10$ lb.

Answer 2

In any system, total mass is conserved. Using this principle, we will derive the amount of prunes we can get from one pound of plums.

Suppose we have 1 pound of plums - this would have 0.92 pounds of water.

Now, when we dry it, suppose we remove $x$ pounds of water. Then the total mass of the system is $1-x$ pounds

Of this, we have $20\%$ water. Hence the final amount of water is $0.2(1-x)$

Now using the conservation of mass of water

$$\text{Total Initial Water mass} = \text{Evaporated water mass} + \text{Final Water Mass}$$

$$0.92 = x + 0.2(1-x)$$

Solve for $x$, and then the weight of prunes is $(1-x$) : because the water is still part of the prune, so you would not take 80% of this