Let's define the cost of the laptop as [tex]\( x \)[/tex].
### Step-by-Step Breakdown:
1. Savings in the First Month:
Kavitha saved [tex]\(\frac{1}{3}\)[/tex] of the laptop's cost in the first month. So,
[tex]\[
\text{First month savings} = \frac{x}{3}
\][/tex]
2. Savings in the Second Month:
In the second month, she saved [tex]\( \$ 125 \)[/tex] less than what she saved in the first month. Thus,
[tex]\[
\text{Second month savings} = \frac{x}{3} - 125
\][/tex]
3. Savings in the Third Month:
She saved the remaining [tex]\( \$ 525 \)[/tex] in the third month. So,
[tex]\[
\text{Third month savings} = 525
\][/tex]
### Total Costs:
The total savings over three months equals the cost of the laptop:
[tex]\[
\text{First month savings} + \text{Second month savings} + \text{Third month savings} = x
\][/tex]
Substitute the known values into the equation:
[tex]\[
\frac{x}{3} + \left(\frac{x}{3} - 125\right) + 525 = x
\][/tex]
### Simplify the Equation:
Combine the terms involving [tex]\( x \)[/tex]:
[tex]\[
\frac{x}{3} + \frac{x}{3} - 125 + 525 = x
\][/tex]
[tex]\[
\frac{2x}{3} + 400 = x
\][/tex]
Isolate [tex]\( x \)[/tex] by subtracting [tex]\(\frac{2x}{3}\)[/tex] from both sides:
[tex]\[
400 = x - \frac{2x}{3}
\][/tex]
[tex]\[
400 = \frac{3x}{3} - \frac{2x}{3}
\][/tex]
[tex]\[
400 = \frac{x}{3}
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 400 \times 3
\][/tex]
[tex]\[
x = 1200
\][/tex]
Thus, the cost of the laptop is [tex]\( \boxed{1200} \)[/tex] dollars.
