When famke charges her phone, it gains 2 percentage points each minute. when frmke uses her phone, it loses 5 percentage points each minute. once, famke used her phone for some time, and then charged it for twice the amount of time she used it. in the end, her phone lost 10 percentage points. how long did famke use her phone and how long did she charge it?

If t is the amount of time she used it, then it lost t*(5/min) percentage points; then she charged it for 2t, so it gained (2t)*(2/min) =t*(4/min) percentage points.
This means that above this time period, the phone lost t*(5/min)-t*(4/min) =t*(1/min) percentage points; because this loss is recognized to be 10 percentage points, this means t*(1/min) =10, so t=10 min.
This means that she used her phone for 10 minutes and charged it for 20 minutes.

It's like discovering the answer to a puzzle. the purpose in solving an equation is to find the value or values of the variable that makes it a true statement. any value of the variable that makes the equation true is called a solution to the equation.