The sum of pete's and sam's ages is 30. five years ago, pete was 3 times as old as sam. how old is sam? let p = pete's age, s = sam's age, and p + s = 30. which of the following equations would complete the system?

a. p - 5 = 3s
b. p - 5 = 3s - 5
c. p - 5 = 3s - 15

Five years ago:
Peter= P-5
Sam = S-5
Peter was 3 times older than Sam, which means that (P-5) = 3(S-5)
P-5 = 3S-15
So, the equation that would complete the system is C. P - 5 = 3S - 15

P-5 = 3S-15
P-3S = -15+5
P-3S = -10

So, now we use two equations: P-3S = -10 and the original one P+S=30
P-3S=-10
P+S=30 (to simplify the equation, multiply it by -1)

P-3S=-10
-P-S=-30

0P-4S=-40
-4S=-40
4S=40
S=40/4
S=10

P+S=30
P+10=30
P=20

This means that Pete is 20, and Sam is 10. Hope this helps!