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! :)