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

Question

contestada

Respuesta :

hitthequanaf hitthequanaf · Answer 1 · 2017-06-12T20:39:14+02:00

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 Link

Alleei Alleei · Answer 2 · 2020-01-14T09:38:08+01:00

Answer : The equation complete the system is, [tex]P-5=3S-15[/tex] 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:

[tex]P+S=30[/tex] ..............(1)

[tex]P=30-S[/tex] ..............(A)

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

[tex](P-5)=3\times (S-5)[/tex] ..............(2)

[tex]P-5=3S-15[/tex]

Now substituting equation A in equation 2, we get:

[tex](P-5)=3\times (S-5)[/tex]

[tex](30-S-5)=3\times (S-5)[/tex]

[tex]30-S-5=3S-15[/tex]

[tex]30+15-5=3S+S[/tex]

[tex]40=4S[/tex]

[tex]S=\frac{40}{4}[/tex]

[tex]S=10[/tex]

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

[tex]P=30-S[/tex]

[tex]P=30-10[/tex]

[tex]P=20[/tex]

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

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