equations, inequalities, and problem solving?

Question

the sum of the present ages of angie and her mother is 64. in eight years angie will be three-fifths as old as her mother at that time. find the present ages of angie and her mother.

whoever answers this please explain it fully and how i come up with a formula

Answer 1

Angie is x, Mom is y,

1) x + y = 64,

2) (x + 8) = (3/5) (y+8)

from 1),
y = 64 - x,

from 2),
y = (5/3)(x + 8) - 8

then,
(5/3)(x + 8) - 8 = 64 - x

solving for x,
(5/3)x + x = 64 - (5/3)8 + 8
8/3 x = 176/3
x = 176 / 8 = 22, which is Angie´s age

from 1), y = 64 - 22 = 42, which is Mom´s age

Answer 2

x + y = 64
(x + 8) = 3 (y + 8) / 5

x + y = 64
x + 8 - 3y / 5 = 3 * 8 / 5

x + y = 64
x -3y / 5 = 24 / 5 - 8

5x + 5y = 320
5x - 3y = 24 - 40

5x + 5y = 320
5x - 3y = -16

5x + 5y = 320
-5x + 3y = 16

Now, the crucial step...add the two equations together:

8y = 336

y = 42. Angie's mother is 42.
64 - 42 = 22. Angie is 22.

Check:
In 8 years, Angie will be 30.
In 8 years, Angie's mother will be 50.
30 is three-fifths of 50.

Answer 3

angie + mother =64.........(1)

8 years later....
Angie+8=3/5(mother+8) .......(2)

from these 2 equation....
We can eliminate one variable(either Angie or mother)...
(In this case I eliminate Angie)
16= 3mother-5 Angie........(2)
64= mother+ Angie.......(1) ---> 320= 5Mother+5 Angie

then we get ....336=8mother
mother=42
then simply subtract mother years to find Angie one...
Angie=64-42=22

Answer 4

A + M = 64; A + 8 = 0.6(M + 8). Recast the first equation as M = 64 - A, and substitute to get:
A + 8 = 0.6((64-A) + 8). Then:
A + 8 = 38.4 - 0.6A +4.8;
1.6A = 35.2; A = 22; M = 42.

Answer 5

i just noticed i'm in mathematics - oops not my thing.
good luck.