Final answer:
To find the ages of Jack and Priscilla, we set up equations based on the given information that Jack is 7 years older and together their ages total 157 years. Solving these equations, we find Priscilla's age to be 75 years old, and Jack's age to be 82 years old.
Step-by-step explanation:
Let's denote Jack's age as J and Priscilla's age as P. According to the problem, Jack is 7 years older than Priscilla, which means we can write J = P + 7. It's also given that their combined ages total 157 years, so we can write the equation J + P = 157. Substituting the first equation into the second gives us (P + 7) + P = 157. Simplifying this equation yields 2P + 7 = 157, and subtracting 7 from both sides gives 2P = 150. Dividing both sides by 2 gives us P = 75. Now we know Priscilla's age, and we can find Jack's age by adding 7, which gives us J = 82. Therefore, Priscilla is 75 years old and Jack is 82 years old.