The sum of a non-zero number and thrice its reciprocal is
7
52
​
. Find the number.

Let the non-zero number be x.
According to the problem description:

x+3(
x
1
​
)=
7
52
​

x+
x
3
​
=
7
52
​

Combine terms on the left hand side:

x
x
2
+3
​
=
7
52
​

Cross-multiply to formulate a quadratic equation:

7(x
2
+3)=52x
7x
2
+21=52x
7x
2
−52x+21=0
Solve this quadratic equation using factorization (splitting the middle term):

7x
2
−49x−3x+21=0
7x(x−7)−3(x−7)=0
(7x−3)(x−7)=0
This yields two possible values for x:

x=7orx=
7
3
​

Looking at the options, 7 is present as Option C.