Final answer:
Juwan's age equation J = 2P + 5 and Peyton's age equation P = J - 10 are solved simultaneously to find that Juwan is 15 years old and Peyton is 5 years old. The sum of their ages is 20 years.
Step-by-step explanation:
Let's denote Juwan's age as J and Peyton's age as P. According to the problem, Juwan's age is 5 more than 2 times Peyton's age. This can be expressed as J = 2P + 5. It is also given that Peyton's age is 10 years less than Juwan's age, which can be written as P = J - 10.
Now, let's substitute the value of P from the second equation into the first equation, J = 2(J - 10) + 5. Simplifying the equation, we get J = 2J - 20 + 5, which leads to J - 2J = -20 + 5. After further simplification, we get -J = -15, so J = 15 years.
Using the value of J in the second equation, P = 15 - 10, which gives us P = 5 years. Therefore, the sum of the ages of Juwan and Peyton is J + P = 15 + 5 = 20 years.