For her parents' 50th wedding anniversary celebration, Malina decides to buy $50$ balloons. Her supplier only sells balloons in bunches of $12$ for $\text{Rs. }250$ and bunches of $7$ for $\text{Rs. }175$. Malina buys exactly $50$ balloons. What is the total price she pays?

Let $x$ be the number of bunches of $12$ balloons, and $y$ be the number of bunches of $7$ balloons.
Since she buys exactly $50$ balloons:

$$12x+7y=50$$

Since $x$ and $y$ must be non-negative integers:
If $x=0⟹7y=50$ (not an integer)
If $x=1⟹12+7y=50⟹7y=38$ (not an integer)
If $x=2⟹24+7y=50⟹7y=26$ (not an integer)
If $x=3⟹36+7y=50⟹7y=14⟹y=2$
If $x=4⟹48+7y=50⟹7y=2$ (not an integer)

Thus, the only valid integer solution is $x=3$ bunches of $12$ balloons and $y=2$ bunches of $7$ balloons.
The total price paid is:

$$\text{Total Price}=(3\times 250)+(2\times 175)=750+350=\text{Rs. }1100$$