Amother is 30 years older than her twin daughters. in 2 years her age will be three times the combined ages of the twins. how old are the twins right now ?

The twins are 4 years old right now.

mother's age = x
daughters' age = y

mother is 30 years older than her twin daughters:
x = y + 30
in 2 years, her age will be 3 times the combined ages of the twins (twins will also be 2 years older)
x + 2 = 3 × (2(y + 2))
*2(y + 2) because there are 2 daughters
now we simplify the equation:
x + 2 = 3 × (2(y + 2))
x + 2 = 3 × (2y + 4)
x + 2 = 6y + 12
x = 6y + 10

now we have 2 equations:
x = y + 30
x = 6y + 10
to solve for y ( the age of the twins right now), substitute the "x" in one of the equations with the "y statement" of the other equation so no x is present:
x = y + 30
(6y + 10) = y + 30
solve for y
6y + 10 = y + 30
5y + 10 = 30
5y = 20
y = 4 ( the daughters are 4 years old right now)
if their mother is 30 years older than them, then she is 34 (x = 34)

check answers by inputting x and y values in either equation:
x = y + 30
34 = 4 + 30
34 = 34 ✔

x + 2 = 3 × (2(y + 2))
34 + 2 = 3 × (2(4 + 2))
36 = 3 × (2(6))
36 = 3 × 12
36 = 36 ✔