Converting grapes to raisin

Since dried grapes contain 16% water. 10 kg of dried grapes contain 1.6 kg of water and 8.4 kg of grapes or $W_{\text{grapes}} = 8.4$ kg. Let the needed weight of fresh grapes be $W$ . Since fresh grapes contain 88% water or 12% grapes, then $\dfrac {W_{\text{grapes}}}W = 0.12 \implies W = \dfrac {W_{\text{grapes}}}{0.12} = \dfrac {8.4}{0.12} = \boxed{70}$ kg.

Assume that $x =$ Amount in kg of the fresh grapes to be used

$x\times (1-0.88) + 10\times 0.16) = 10 \ \ kg \\ x = 70 \ \ kg$

Similar but slightly different: Let the net weight (water and fruit) of the grapes be $x$ . Then the fruit content of the fresh grapes is $0.12x$ , and that of the dried grapes is $0.84 \times 10$ . Since the mass of the fruit content does not change (only water is lost due to evaporation), then $0.12x = 0.84 \times 10 \Rightarrow x = 70$ kg.

And here is Mahmoud Khattab's solution expressed slightly differently: the fresh grapes have water : fruit equal to $88:12 = 22:3$ , and the dried grapes have a ratio of $16:84 = 4:21$ . Since the fruit content does not change, $3$ parts of the fresh grapes is equal to $21$ parts of the dried grapes, which means that $1$ part of dried grapes is equal to $\frac{3}{21} = \frac{1}{7}$ of the fresh grapes. Hence the mass of the fresh grapes is $\frac{10}{1/7} = 70$ kg again.

• Considering grapes consist of flesh (F) & water (W).
• Before drying grapes (G) consists of 88% W & 12% F.
• After drying grapes (G') consists of 16% W & 84% F.
• Since flesh content before drying = flesh content after drying.

So

12%G=84%G' ⟹ G=7G' ⟹ G=7×10=70