Question
When Famke charges her phone, it gains 2 percentage points each minute. When Famke 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?

Right answer
Famke used her phone for 10 minutes, and charged her phone for 20 minutes.

Solution
The total percentage points lost when Famke used her phone can be modeled by 5x, and the total percentage points gained when Famke charged her phone can be modeled by 2y. In the end, her phone lost 10 percentage points. This gives us the following equation:
−5x+2y=−10
We are also given that Famke used her phone for some time and then charged it for twice the amount of time she used it. This can be expressed as:
y=2x
Now that we have a system of two equations, we can go ahead and solve it!