Question

After graduation, Rob got job offers from two different companies. Printer Palace offered him $3,500 per month, plus a $7,000 signing bonus. East Company Paper offered him $4,500 per month, with no signing bonus.
How many months would Rob need to work for his total earnings to be the same at either company?
months

Answer 1

To determine how many months Rob needs to work for his total earnings to be the same at both companies, we can set up an equation.

Let's denote the number of months Rob works as \( x \).

1. **Earnings at Printer Palace**:
- Monthly salary: $3,500
- Signing bonus: $7,000
- Total earnings after \( x \) months:
\[
\text{Total earnings} = 3500x + 7000
\]

2. **Earnings at East Company Paper**:
- Monthly salary: $4,500
- Total earnings after \( x \) months:
\[
\text{Total earnings} = 4500x
\]

Now we set the total earnings from both companies equal to each other:
\[
3500x + 7000 = 4500x
\]

Next, we can isolate \( x \):
1. Subtract \( 3500x \) from both sides:
\[
7000 = 4500x - 3500x
\]
\[
7000 = 1000x
\]

2. Now, divide both sides by 1000:
\[
x = \frac{7000}{1000} = 7
\]

Rob would need to work for **7 months** for his total earnings to be the same at either company.