Can Dancing While Eating Keep You Thin? A Mathematical Model of Weight Change

1 Problem Statement

We ask how the blogger’s weight changes under a “dance‑eat‑dance” lifestyle, requiring a model of calorie intake, expenditure, and weight gain.

2 Model Assumptions

The blogger’s basal metabolic rate (BMR) is constant.

Calorie intake per meal and calories burned per dance session can be estimated.

7700 kcal surplus corresponds to 1 kg weight gain.

3 Model Formulation

A differential equation describes the dynamics of weight W(t):

Calorie intake – assumed fixed per recommended dish.

Calorie expenditure – calories burned during each dance.

Metabolic rate – BMR in kcal per day.

The resulting equation relates daily net calories to weight change.

4 Model Analysis

Solving the equation shows that if net calories are positive, weight increases; if negative, weight decreases.

5 Case Study

Assume a 30‑year‑old male blogger, 180 cm tall, 70 kg, who posts one meal per week and dances before and after it. Using the revised Harris‑Benedict formula, his BMR ≈ 1719.66 kcal/day.

Dance burns about 5 kcal per minute; with 5 minutes total per episode, each session burns ≈25 kcal.

Each bowl of “large intestine noodles” provides ≈900 kcal.

Other net daily calories are assumed to be 1800 kcal.

He recommends two meals per week, so the weekly net surplus is calculated and the differential equation is iterated over 12 weeks.

The simulation predicts an average weekly weight gain of about 0.73 kg, leading to roughly 9 kg increase after three months if the lifestyle remains unchanged.

The model relies on simplified assumptions; real weight change is affected by many additional factors such as variable metabolism, thermic effect of food, nutrient composition, and adaptive responses to exercise.

While the model offers a quantitative illustration of how excess intake over expenditure leads to weight gain, it should be taken as a rough estimate rather than a precise prediction.