Question

Macy doesn’t have any money in her bank account, but begins saving $15 each week. Robby has $20 in his bank account and saves $10 each week. After how many weeks will Macy and Robby have the same amount in their accounts?

Macy doesn’t have any money in her bank account, but begins saving $15 each week. Robby has $20 in his bank account and saves $10 each week. After how many weeks will Macy and Robby have the same amount in their accounts?

Answer 1

Let's denote the number of weeks as \( w \).

Macy starts with $0 and saves $15 each week, so the amount of money Macy has after \( w \) weeks can be expressed as:

\[
M(w) = 15w
\]

Robby starts with $20 and saves $10 each week, so the amount of money Robby has after \( w \) weeks can be expressed as:

\[
R(w) = 20 + 10w
\]

We want to find the value of \( w \) when Macy and Robby's amounts are equal:

\[
15w = 20 + 10w
\]

Now, we will solve this equation for \( w \).

1. Subtract \( 10w \) from both sides:

\[
15w - 10w = 20
\]

This simplifies to:

\[
5w = 20
\]

2. Now, divide both sides by 5:

\[
w = \frac{20}{5} = 4
\]

Thus, they will have the same amount in their accounts after **4 weeks**. We can verify this by calculating the amounts after 4 weeks:

- Macy's amount after 4 weeks:

\[
M(4) = 15 \times 4 = 60
\]

- Robby's amount after 4 weeks:

\[
R(4) = 20 + 10 \times 4 = 20 + 40 = 60
\]

Both amounts equal $60, confirming our solution. Therefore, the answer is:

**4 weeks**.