To solve this problem, you can use a system of equations to represent the information given in the problem.
First, let's let "a" represent Ashton's age and "j" represent Jerome's age.
Next, we can set up the first equation based on the information that Jerome is 7 years younger than Ashton:
j = a - 7
We can also set up the second equation based on the information that Jerome is half Ashton's age:
j = (1/2)a
Now we have a system of equations that we can solve to find the ages of both boys. To solve for "a," we can substitute the second equation into the first equation:
a - 7 = (1/2)a
This simplifies to:
(1/2)a - 7 = (1/2)a
Subtracting (1/2)a from both sides gives us:
(-1/2)a - 7 = 0
Multiplying both sides by (-2) gives us:
a = 14
Now that we know Ashton is 14 years old, we can use either equation to find Jerome's age. Substituting 14 for "a" in the first equation gives us:
j = 14 - 7
Which simplifies to:
j = 7
Therefore, Ashton is 14 years old and Jerome is 7 years old.