$1.$There are $1000$ kg of a $60\%$ pineapple juice concentrate, and it is desired to mix it with $1000$ lb of water to dilute it$.$ What is the final concentration of the juice and how many pounds are there in total?

$2.$How many pounds of water must be evaporated to concentrate $200,000$ lb$/$h of tomato juice from $2\%$ to $40\%$ solids?

$3.$What will be the final concentration of a juice from which $10,000$ lb of water is removed, if initially there were $950,000$ lb of juice with a water content of $60\%?$