By weight, raspberries are 85% water, raspberry jam is 30% water, and sugar contains no water. I make raspberry jam by mixing equal weights of raspberries and sugar and then boiling them to evaporate off some of the water.
What weight of jam can I make with 2.8 kg of raspberries?
If $x$ is the final amount of jam produced, then final amount of water $w = 0.30x$
Final amount of water $w$ is some percentage $n$ of the water in raspberries $= (2.8*0.85)n\\ ⇒ 0.30x = 2.38n$
Final amount of jam = amount of raspberries without water + amount of water from raspberries + sugar.
so, $x = 2.8*0.15 + 2.38n + 2.8\\ ⇒ x = 2.38n + 3.22$
Solving, $x = 2.38 * \frac{0.30}{2.38}x + 3.22\\⇒x = 4.6$
So 4.6 kg of jam can be produced from 2.8kg of raspberries.
Is that correct and using an efficient technique?
I mention "efficient technique" because i often spend a lot of time going round in circles trying to relate facts in algebra.
Your method seems correct, but it can be done more straightforwardly.
You have $2.8$ kg of rasperries, of which $0.85\cdot2.8 = 2.38$ kg is water, and the remaining $2.8-2.38=0.42$ kg is non-water.
After adding the $2.8$ kg of sugar, you still have have $2.38$ kg water, but now have $0.42+2.8=3.22$ kg of non-water.
After evaporating some water to make the jam, the water is $30\%$ of the whole, so the non-water must be $70\%$ of the whole amount of jam. If $x$ is the whole amount of jam, $3.22$ kg is $70\%$ of $x$, then we get $0.70\ x = 3.22$, or $x=4.6$ kg of jam.