Answer
She would take 493 days to get to a BMI of 20.
Work Step by Step
Energy contents:
Pizza: 350 Cal/slice
Coke: 87 Cal/200ml
The difference in habits is 1 slice of pizza and 200 ml of coke less, hence $\Delta E = -437\ Cal/day$
The energy content of fat is 33.1 MJ/kg, so:
$\Delta \dot{m} = -0.0553\ kg/day$
The difference in weight would be ($H=1.6m$) :
$\Delta m = -H²(BMI_2-BMI_1)=-25.6\ kg$
The total time for this weight loss would be:
$\Delta t = 462.93\ days$
She would take 493 days to get to a BMI of 20.
