Question

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?

P - 5 = 3S
P - 5 = 3S - 5
P - 5 = 3S - 15

Answer 1

P-5=3s-15 because Pete is 20 and Sam is 10. 20-5= 15 and 3(10)-15 also equals 15. The answer is C.

Answer 2

Answer : The equation complete the system is,
`P-5=3S-15` and the Sam is 10 years old.

Step-by-step explanation :

As we are given that sum of Pete's and Sam's ages is 30. Thus, the equation will be:

`P+S=30` ..............(1)

`P=30-S` ..............(A)

And, five years ago, Pete was 3 times as old as Sam. Thus, the equation will be:

`(P-5)=3* (S-5)` ..............(2)

`P-5=3S-15`

Now substituting equation A in equation 2, we get:

`(P-5)=3* (S-5)`

`(30-S-5)=3* (S-5)`

`30-S-5=3S-15`

`30+15-5=3S+S`

`40=4S`

`S=(40)/(4)`

`S=10`

Now put the value of 'S' in equation A, we get the value of 'P'.

`P=30-S`

`P=30-10`

`P=20`

The age of Pete is, 20 and the age of Sam is, 10

Thus, the equation complete the system is,
`P-5=3S-15` and the Sam is 10 years old.