For Mistake To Be Lossless...

What was the mistake?

Let's assume that those things costs a and b respectively.

As per Bob's wrong calculation,

a / b = 5.25

a = 5.25 b  ..........(1)

And according to what should have been correct,

a + b = 5.25

Putting (1) in above,

5.25b + b  = 5.25

6.25b = 5.25

b = 0.84

Again putting this value in (1) gives,

a + 0.84 = 5.25

a = 5.25 - 0.84

a = 4.41

 
Hence the cost of 2 things are $4.41 and $0.84.