On serena's 10th birthday her mom was 3 times serena's age. how old will serena and her mom be when her mom's age time 0.5 equal serena's age

When serena was 10 and her mom was 3 times her age that means they are 20 years apart from each other so when serena is 20 she will be half her moms age because her mom will be 40.

Mom is 3 times of serena
3*10=30
mom is 30

when will serena's age be half of mom's age?

serena's age in x years is 10+x
mom's age in x years is 30+x

find the value that makes this statement true
0.5(30+x)=10+x
solve
so
distribute
15+0.5x=10+x
minus 0.5x from both sides
15=10+0.5x
minus 10 from both sides
5=0.5x
times 2 both sides
10=x

in 10 years
10+10=20
when serena is 20 years old, her mom will be 40