To solve this word problem, let's analyze the given information step-by-step:
1. Distance Up River:
- Jen and Marcus traveled 13 miles up river before they ran out of gas. This represents their travel distance in one direction.
2. Distance Down River:
- After running out of gas, they floated back 12 miles down river before reaching the shore. This represents their travel distance in the opposite direction.
3. Total Distance Traveled:
- To find the total distance they covered, we need to add the distance they initially traveled up river to the distance they floated back down river. By adding these two distances, we can find the total distance they traveled before reaching the shore.
So, we write the number sentence for the total distance as follows:
[tex]\[ 13 \text{ miles (up river)} + 12 \text{ miles (down river)} = 25 \text{ miles (total distance)} \][/tex]
Therefore, the correct number sentence that matches this word problem is:
[tex]\[ A. \ 12 + 13 = 25 \][/tex]
Thus, the answer is [tex]\( \boxed{A \: 12 + 13 = 25} \)[/tex].
