How old are they?

Question

I found this question online. Please help me understand where I may have made a mistake. Thanking you in advance.
My question:
Norman is now 4 times the age of her son, 3 years ago, the sum of their ages was 49. How old are they now?.
My Answer:
First step:
(The sum of their age 3 years ago was 49).
Answer:
2 ➗ 24 is 12, with a remainder of 1.
Since, there's 2 people, I divided the remainder 1 into half, and then added 1/2 to both of their age.
Step 2:
Next, (I took the 24➗ 2 people equal's 12 with a remainder of 12)
Answer:
So, I figured that Normans' son is now 12 and 1/2 years old.
Step 3:
I then,( multiplied the remainder of 12.
12✖ 4(Norman's age is 4❌ her son age).
12✖ 4 equal 48.
Finale Step:
(I added Norman's age48, plus the 3 years ago, plus the extra 1/2 year from the remainder of 1 that was divided into 1/2 to figure her now age).
Answer:
48➕ 3➕ 1/2 equals Norman now age which is 51, and 1/2 years old.

My Finale Answer to how old are they now?:
Answer: Norman's age now is 51 and 1/2 years old, and her sons age is 12 and 1/2 years old.

Answer 1

Let
N = Norman's age
S = her son's age

Norman is now 4 times older than her son.
N = 4S

Three years ago, the sum of their ages was 49.
(N - 3) + (4S - 3) = 49

Substitute N for 4S. Solve for S.
4S - 3 + 4S - 3 = 49
...
S = 6.875

Thus...

N = 4(6.875) = 27.5

Therefore, Norman's age is 27.5 (or 27 and 1/2) and her son's age is 6.875 (or 6 and 7/8).

Answer 2

Now:
son's age --- x
Norman's age --- 4x

Three years ago:
son ---- x-3
Norman --- 4x-3

so x-3 + 4x-3 = 49
5x = 55
x = 11

the son is now 11 and Norman is 44

check:
3 years ago, son was 8 and Norman was 41
what is 41 + 8 ??

Answer 3

Thanks' Reiny,for your help in solving, and simplifying my problem.
And to answer your check question to me, 41➕ 8 is 49 😊

Answer 4

Thanks, herp derp,😊 for clarifying my math problem in reference to Norman and her sons now, ages.