Explanation:

- We are given three coprime numbers $a$, $b$, and $c$.

- The product of the first two numbers is $a\times b=88$.

- The product of the last two numbers is $b\times c=165$.

- To solve, list the factors of 88 and 165:

- 88 = 2^3 × 11

- 165 = 3 × 5 × 11

- Factors shared by the two products is 11, pointing to:

- $b=11$

- Calculate $a$ using $a\times 11=88$ ? $a=8$.

- Calculate $c$ using $11\times c=165$ ? $c=15$.

- Sum: $a+b+c=8+11+15=34$.

- Options:

- 1) 44

- 2) 38

- 3) 36

- 4) 34