The sum of the ages of petra and her mother is 53. her mother is 11 years more than twice as old as petra. how old are petra and her mother?

Set up a system of equation:
p+m=53
m=2p+11

Use the substitution method to for "m"
p+(2p+11)=53
3p+11=53
3p=42
p=14

Put "p" into either equation to solve for "m"
m=2(14)+11
m=28+11
m=39

Check by plugging both "p" and "m" into both equations to make sure they work:
14+39=53
53=53
That one works, now let's check the other one
39=2(14)+11
39=28+11
39=39
They both work!
Petra is 14 years old, and her mother is 39 years old