y varies partly as x, partly inversely as x and partly constant. the graph of y againts x through the points (2.20), (3.16), and (5,14). Find a general formula for y in terms of x

Answer 1

y = ax + b/x + c

where a, b, and c are constants.

Answer 2

to find the particular values of a,b,c use
2a + b/2 + c = 20
3a + b/3 + c = 16
5a + b/5 + c = 14
solve those to get
y = x + 30/x + 3

Answer 3

Now finishing the question: plug in the 3 points
20 = 2a + b/2 + c or 40 = 4a + b + 2c
16 = 3a + b/3 + c or 48 = 9a + b + 3c
14 = 5a + b/5 + c or 70 = 25a + b + 5c

subtract the 1st from the 2nd -> 5a + c = -4
subtract the 2nd from the 3rd -> 16a + 2c = -2

double 5a + c = -4 to get 10a + 2c = -8
subtract from 16a + 2c = -2
6a = 6
a = 1

back in 5a + c = -4
c = -9

back into the first:
4a + b + 2c = 20
4 + b - 18 = 20
b = 34

y = x + 34/x - 9