Question

Natasha starts with $45 in her savings account and each month she at $6 sal starts with $55 in his saving account and each month he adds $4 how many months will it take for Natasha to have more money in her savings account then selling his Natasha starting amount $45 sal $55 Natasha month 1 $51 sal $59 Natasha month 2 $57 month 2 sal $63 A 4 B 5 C 6 D 7

Answer 1

Let's track the savings for both Natasha and Sal over the months:

Natasha:

• Starting amount: $45
• Monthly addition: $6
• Amount after month \( n \): \( 45 + 6n \)

Sal:

• Starting amount: $55
• Monthly addition: $4
• Amount after month \( n \): \( 55 + 4n \)

We want to find the smallest integer \( n \) for which Natasha's savings exceeds Sal's savings:

\[ 45 + 6n > 55 + 4n \]

Subtract \( 4n \) from both sides:

\[ 45 + 2n > 55 \]

Subtract 45 from both sides:

\[ 2n > 10 \]

Divide by 2:

\[ n > 5 \]

The smallest integer \( n \) that satisfies this is \( n = 6 \).

Therefore, it will take 6 months for Natasha to have more money in her savings account than Sal.

The answer is C. 6.