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?

Answer 1

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:

$(P-5)=3\times (S-5)$     ..............(2)

$P-5=3S-15$

Now substituting equation A in equation 2, we get:

$(P-5)=3\times (S-5)$

$(30-S-5)=3\times (S-5)$

$30-S-5=3S-15$

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

$40=4S$

$S=\frac{40}{4}$

$S=10$

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.

Answer 2

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.