An older person is 3 years older than eight times the age of a younger person the sum of their ages is 48 what are their ages

Let the age of the older person be x, and the age of the younger y.

"An older person is 3 years older than 8 times the age of a younger" can be represented by the equation x = 8y + 3
"The sum of their ages is 48" can be represented by x + y = 48

We can now create a system:
x = 8y + 3 (1)
x + y = 48 (2)

Let's use the value of x in the equation (1) in equation (2) to find the value of y:
x + y = 48
8y + 3 + y = 48
9y + 3 = 48
Subtract 3 from each side to have the variables on a side and the numbers on the other:
9y + 3 - 3 = 48 - 3
9y = 45
Divide both sides by 9 to get y alone on a side and its value on the other side:
(9y)/9 =  45/9
y = 5

Let's replace y by it's value in the equation (1) to find x:
x = 8y + 3 = 8*5 + 3 = 40 + 3 = 43.

So the older person is 43 years old, and the younger person is 5 years old.

You can recheck your answer (very important):
x + y = 43 + 5 = 48 (The sum of their ages is 48)
8y + 3 = 8*5 + 3 = 43 = x (an older is 3 years older than eight times the age of a younger)
The answer has been approved.

Hope this Helps! :)