Question

Beth and her cousin Albert both collect stamps. Beth currently has 80 stamps in her collection, and she adds 4 more each month. Right now, Albert only has 20 stamps in his collection, but he adds 10 more each month.
Which equation can you use to find m, the number of months it will take for Albert to have as many stamps as Beth?
How many months will it take for Albert to have as many stamps as Beth?
months

Answer 1

To determine when Albert will have the same number of stamps as Beth, we can set up equations for both of their collections as a function of the number of months \( m \).

1. **Beth's Collection**:
- Starting amount: 80 stamps
- Amount added each month: 4 stamps
- Total after \( m \) months: \( 80 + 4m \)

2. **Albert's Collection**:
- Starting amount: 20 stamps
- Amount added each month: 10 stamps
- Total after \( m \) months: \( 20 + 10m \)

We want to find when Albert's collection equals Beth's collection. Thus, we can set up the following equation:

\[
20 + 10m = 80 + 4m
\]

Now we can solve for \( m \).

1. First, subtract \( 4m \) from both sides:

\[
20 + 10m - 4m = 80 + 4m - 4m
\]

This simplifies to:

\[
20 + 6m = 80
\]

2. Next, subtract 20 from both sides:

\[
6m = 80 - 20
\]

This simplifies to:

\[
6m = 60
\]

3. Finally, divide both sides by 6:

\[
m = \frac{60}{6} = 10
\]

Therefore, it will take **10 months** for Albert to have as many stamps as Beth.