My mother and I are the same age – only the numbers are reversed (21,12 for example)

Twelve years ago my mom was twice as old as me.
So how old is my mommy and how old am I?

Let the two digits in the ages be x and y. Your mother's age now is 10x + y. Yours is 10 y + x.

Twelve years ago,

10 x + y -12 = 2 (10 y +x-12)
10 x + y = 20y + 2x -12
19y = 8x + 12

Try integers 0 through 9 for y and see which gives an integer for x.
Only this combination works:
y = 4, x = 8

Current ages are 48 and 84.
Twelve years ago they were 36 and 72

mom's age -- 10x + y

daughter ---- 10y + x

10x + y -12 = 2(10y +x - 12)
8x -19y = -12

now both x and y are probably integers, and y has to be less than x
I tried y = 1,2,3,4 and
y = 4 worked
when y = 4, x = 8

so mom is now 84 and the daughter is 48

check :
12 years ago mom was 72
and the daughter was 36 , check!

To determine the ages of both you and your mother, let's break down the given information step by step:

1. You and your mother are the same age, but the numbers are reversed. Let's call your current age "x" and your mother's current age "y". According to the first statement, the digits of your ages are reversed. So, mathematically, this can be represented as: 10x + y = 10y + x.

2. Twelve years ago, your mother was twice as old as you. To handle this part, we need to subtract 12 from both your ages. At that time, your age becomes x - 12 and your mother's age becomes y - 12. Mathematically, this can be represented as: y - 12 = 2(x - 12). Simplifying this equation will give us: y - 12 = 2x - 24.

Now, we have a system of two equations:
Equation 1: 10x + y = 10y + x
Equation 2: y - 12 = 2x - 24

To solve this system, we can use substitution or elimination. Let's use the substitution method to find the ages.

From Equation 1, we can rewrite it as: 9x - 9y = 0.

Now, we solve Equation 2 for y in terms of x:
y = 2x - 12.

Substituting this into Equation 1, we get: 9x - 9(2x - 12) = 0.
Simplifying this equation gives us: 9x - 18x + 108 = 0.
Combining like terms, we have: -9x = -108.
Dividing both sides by -9, we find: x = 12.

Now, substitute this value of x back into Equation 2 to find y:
y = 2(12) - 12 = 24 - 12 = 12.

So, your mother is 12 years old and you are also 12 years old.