To determine the first month in which Jordan will have saved enough money to buy the laptop, we need to find the smallest integer value of [tex]\( m \)[/tex] such that his total savings [tex]\( d \)[/tex] is at least \[tex]$325. The equation given is:
\[ d = 80 + 75m \]
We need to solve for \( m \) when:
\[ 80 + 75m \geq 325 \]
### Step-by-Step Solution:
1. Subtract 80 from both sides of the inequality:
\[
75m \geq 325 - 80
\]
2. Simplify the right-hand side:
\[
75m \geq 245
\]
3. Divide both sides by 75 to solve for \( m \):
\[
m \geq \frac{245}{75}
\]
4. Calculate the value of \(\frac{245}{75}\):
\[
\frac{245}{75} \approx 3.2666666666666666
\]
5. Since \( m \) must be an integer, we round up to the next whole number:
\[
m = 4
\]
### Conclusion:
The smallest integer value of \( m \) that satisfies Jordan's savings to be at least \$[/tex]325 is 4. Therefore, Jordan will have saved enough money to buy the laptop in Month 4.
- Month 2: Not enough
- Month 3: Not enough
- Month 4: Enough
- Month 5: Also enough, but not the first month
Thus, the answer is Month 4.
