To determine how many days the food will last if 25 more soldiers join the group, we need to know:

1. The total amount of food available.
2. The number of soldiers currently in the group.
3. The number of days the food will last for the current number of soldiers.

Let's denote:

• FFF as the total amount of food.
• SSS as the current number of soldiers.
• DDD as the number of days the food will last for SSS soldiers.

The total food consumption per day for SSS soldiers is S×daily food per soldierS \times \text{daily food per soldier}S×daily food per soldier. Therefore, the total food FFF can be expressed as: F=S×daily food per soldier×DF = S \times \text{daily food per soldier} \times DF=S×daily food per soldier×D

When 25 more soldiers join, the total number of soldiers becomes S+25S + 25S+25. Let D′D'D′ be the new number of days the food will last. The new equation for the food consumption is: F=(S+25)×daily food per soldier×D′F = (S + 25) \times \text{daily food per soldier} \times D'F=(S+25)×daily food per soldier×D′

Substituting FFF from the initial equation: S×daily food per soldier×D=(S+25)×daily food per soldier×D′S \times \text{daily food per soldier} \times D = (S + 25) \times \text{daily food per soldier} \times D'S×daily food per soldier×D=(S+25)×daily food per soldier×D′

We can simplify this by canceling out daily food per soldier\text{daily food per soldier}daily food per soldier: S×D=(S+25)×D′S \times D = (S + 25) \times D'S×D=(S+25)×D′

Solving for D′D'D′: D′=S×DS+25D' = \frac{S \times D}{S + 25}D′=S+25S×D

This formula will give you the number of days the food will last after the additional 25 soldiers join.