# math

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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?

• math -

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

• math -

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!

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