A hospital sheet cleaning company uses a giant centrifuge to clean its customer$$s sheets. To do this, sheets arrive in a conveyor belt into the centrifuge, in which a detergent flow with $97\%$ detergent and $3\%$ of impurities is added. This flow is the result of a previous mix in which a pure detergent and a flow with impurities mix together outside the centrifuge with unknown compositions.

From the centrifuge, $2$ flows go out which are: the first one, with sheets with detergent and impurities into an squeezer. From that squeezer a first flow goes out that collects a big amount of detergent from the sheets and that goes again into the centrifuge. $($That would be a third flow into the centrifuge$)$ and another flow goes out made of some sheets with detergent and impurities. From the centrifuge, a second flow goes out made up of impurities and a high amount of detergent $(13\%$ impurities and $87\%$ detergent$).$

The second outflow from the centrifuge feeds a filter in which other $2$ flows go out, the upper which carries the greatest number of impurities and some amount of detergent $(92\%$ impurities and $8\%$ detergent$).$ The lower flow that contains unknown amounts of detergent and impurities that feeds the mix point described before.

Additional information:

The flow with sheets from hospital is made up of $98\%$ sheets and $2\%$ impurities.

It is known that from the second flow from the squeezer, $5\%$ of impurities go out of the flow with sheets from hospital.

For every $100kg$ of sheets from hospital, $25kg$ of detergent of the first from out the first flow from the centrifuge.

For every $100kg$ of sheets from hospital, outside the squeezer, $22kg$ are obtained of pure detergent that feed a third flow into the

centrifuge. As additional information, for every $100kg$ of sheets from hospital, $3kg$ made up the flow made of some sheets with

detergent and impurities.

Find:

The amount of pure detergent that must be added for every $100kg$ of sheets from hospital.

The composition of the lower outflow from the filter that feeds the mix point.

Determine all the unknown flows and compositions.