The real-world problem that can be modeled by the equation \( 23x + 13 = 29 \) is:
Gabriel bought a new pair of shoes for $29. This is $13 more than 23 times the cost of his old shoes.
In this scenario, \( x \) would represent the cost of the old shoes, and the equation captures the relationship where the cost of the new shoes is $13 more than 23 times the cost of the old shoes.
The other options do not fit the equation structure or context given.