Final answer:
To solve this problem, we can set up a system of equations to represent Meg and Jose's ages. By solving the system, we find that Jose is 3 years old and Meg is 15 years old.
Step-by-step explanation:
To solve this problem, we can set up a system of equations. Let's say Meg's age is represented by M and Jose's age is represented by J. We are given that Meg's age is 5 times Jose's age, so we can write the equation: M = 5J. We are also given that the sum of their ages is 18, so we can write the equation: M + J = 18.
We can use the first equation to express Meg's age in terms of Jose's age. Substituting this into the second equation, we get: 5J + J = 18. Combining like terms, we have: 6J = 18. Dividing both sides by 6, we find: J = 3.
Now that we know Jose's age is 3, we can substitute this value into the equation M = 5J to find Meg's age. Meg's age is 5 times Jose's age, so Meg's age is: M = 5(3) = 15. Therefore, Jose is 3 years old and Meg is 15 years old.