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 $$ =3 S-15 $$ $$ P-5=3 S-5 $$ $$ P \cdot 5=3 S $$

Question

UpStudy AI · Accepted Answer

To solve this problem, we need to set up a system of equations based on the given information.

Given:
1. The sum of Pete's and Sam's ages is 30: $$ P + S = 30 $$
2. Five years ago, Pete was 3 times as old as Sam: $$ P - 5 = 3(S - 5) $$

We need to find the age of Sam, which is represented by $$ S $$.

Let's start by setting up the system of equations:

1. $$ P + S = 30 $$
2. $$ P - 5 = 3(S - 5) $$

Now, we can solve this system of equations to find the age of Sam.
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
  $$\left\{ \begin{array}{l}P+S=30\P-5=3\left(S-5ight)\end{array}ight.$$
- step1: Solve the equation:
  $$\left\{ \begin{array}{l}P=30-S\P-5=3\left(S-5ight)\end{array}ight.$$
- step2: Substitute the value of $$P:$$
  $$30-S-5=3\left(S-5ight)$$
- step3: Simplify:
  $$25-S=3\left(S-5ight)$$
- step4: Expand the expression:
  $$25-S=3S-15$$
- step5: Move the expression to the left side:
  $$-S-3S=-15-25$$
- step6: Add and subtract:
  $$-4S=-15-25$$
- step7: Add and subtract:
  $$-4S=-40$$
- step8: Change the signs:
  $$4S=40$$
- step9: Divide both sides:
  $$\frac{4S}{4}=\frac{40}{4}$$
- step10: Divide the numbers:
  $$S=10$$
- step11: Substitute the value of $$S:$$
  $$P=30-10$$
- step12: Calculate:
  $$P=20$$
- step13: Calculate:
  $$\left\{ \begin{array}{l}P=20\S=10\end{array}ight.$$
- step14: Check the solution:
  $$\left\{ \begin{array}{l}P=20\S=10\end{array}ight.$$
- step15: Rewrite:
  $$\left(P,Sight) = \left(20,10ight)$$
The solution to the system of equations is $$ P = 20 $$ and $$ S = 10 $$.

Therefore, Sam is 10 years old.
Sam is 10 years old.

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 \( =3 S-15 \) \( P-5=3 S-5 \) \( P \cdot 5=3 S \)

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions