Two friends, Sam and Alex, are saving money. Sam starts with $20 and saves $5 per week. Alex starts with $40 and saves $3 per week. After how many weeks will they have the same amount of money? * A. 6 B. 27 C.10 D. 4

Answer 1

Let's set up equations for the amount of money Sam and Alex have after \( w \) weeks.

For Sam:

• Starts with $20 and saves $5 per week.
• After \( w \) weeks, Sam's total amount is given by: \[ S(w) = 20 + 5w \]

For Alex:

• Starts with $40 and saves $3 per week.
• After \( w \) weeks, Alex's total amount is given by: \[ A(w) = 40 + 3w \]

We want to find out when \( S(w) = A(w) \): \[ 20 + 5w = 40 + 3w \]

Now, let's solve this equation step by step.

1. Subtract \( 3w \) from both sides: \[ 20 + 5w - 3w = 40 \] \[ 20 + 2w = 40 \]

2. Subtract 20 from both sides: \[ 2w = 20 \]

3. Divide by 2: \[ w = 10 \]

Thus, after 10 weeks both Sam and Alex will have the same amount of money.

The answer is C. 10.