Peter the optician sees 16 patients one Tuesday. 4 are neither short nor long sighted, the total number of short sighted patients is 2 more than the total number of long sighted, how many patients can be short sighted, how many long sighted, and how many will require varifocal lenses

Number of patients having longsightedness = 5Number of patient having shortsightedness = 7Patients requiring varifocal lenses will be = 12

Solution:

Number of patients having neither long nor shortsightedness = 4

Let number of patients having long sightedness be "x"

The total number of short sighted patients is 2 more than the total number of long sighted

Therefore,

Number of patient having shortsightedness = x + 2

Peter the optician sees 16 patients one Tuesday

Total number of patients = 16

Therefore,

x + x + 2 + 4 = 16

2x + 6 = 16

2x = 16 - 6

2x = 10

x = 5

Number of patients having longsightedness = x = 5

Number of patient having shortsightedness = x + 2 = 5 + 2 = 7

Patients requiring varifocal lenses will be = 5 + 7 = 12