Final answer:
The correct equation to express the relationship that in 16 years, Juan will be 3 times the age that José is now, with José's current age represented by J, is J+16 = 3J. This matches option B and others are mathematically incorrect by either incorrectly structuring the relationship or failing to show any age change.
Step-by-step explanation:
To solve the problem: In 16 years, Juan will be 3 times the age that José is now. If José's current age is represented by J, we set up an equation to express the relationship between Juan's age in 16 years and José's current age. We denote Juan's future age as J+16 (since that is Juan's age in 16 years). We are told that this age is 3 times José's current age, so we have the equation: J+16 = 3×J Looking at the provided options, this equation matches option B, making it the correct answer. To further explain, options A and C incorrectly add 16 to both sides of the equation, and option D only states that J will be equivalent to J+16, which is mathematically incorrect because it suggests José's age does not change over 16 years.