Final answer:
Jason's current age is 8 years. This was determined by setting up an equation to represent the relationship between his and his mother's ages now and in 16 years and then solving for 'x'.
Step-by-step explanation:
The question involves the mathematics concept of setting up and solving an equation based on the given situation about Jason's and his mother's ages. To find Jason's current age, we let x be Jason's current age. According to the question, Jason's age is 1/4 of his mom's current age. This means his mom's age is 4x. In 16 years, Jason will be x + 16 years old and his mom will be 4x + 16 years old. At that time, his age will be 1/2 of his mom's age. So we can set up the equation (x + 16) = 1/2 (4x + 16) and solve for x.
First, we distribute the 1/2 across the parenthesis:
x + 16 = 2x + 8. Next, we simplify and move all the x terms to one side:
16 - 8 = x. This simplifies to:
x = 8. Therefore, Jason's current age is 8 years.