Question

andre and elena are each saving money. andre starts with $100 in his savings account and adds $5 per week. elena starts with $10 in her savings account and adds $20 each week.
part 1: after four weeks, who has more money in their savings account? explain how you know.
part 2: after how many weeks will andre and elena have the same amount of money in their savings accounts.

Explanation:

Part 1

Step1: Calculate Andre's savings

Andre starts with $100 and adds $5 per week. After 4 weeks, his savings is $100 + 5\times4$.
$100 + 5\times4 = 100 + 20 = 120$ dollars.

Step2: Calculate Elena's savings

Elena starts with $10 and adds $20 per week. After 4 weeks, her savings is $10 + 20\times4$.
$10 + 20\times4 = 10 + 80 = 90$ dollars.

Step3: Compare the two amounts

Since $120 > 90$, Andre has more money after 4 weeks.

Step1: Define the variable

Let $w$ be the number of weeks.

Step2: Write the equations for savings

Andre's savings: $A = 100 + 5w$
Elena's savings: $E = 10 + 20w$

Step3: Set the equations equal (same amount)

$100 + 5w = 10 + 20w$

Step4: Solve for $w$

Subtract $5w$ from both sides: $100 = 10 + 15w$
Subtract 10 from both sides: $90 = 15w$
Divide both sides by 15: $w = \frac{90}{15} = 6$

Answer:

Andre has more money in his savings account after four weeks.

Part 2