Đặt số lượng bút mua là x, số lượng quyển vở mua là y.

Theo đề bài, ta có hai phương trình:

x + y = ? (1)

17x + 5y = 165 (2)

Để giải hệ phương trình này, ta có thể sử dụng phương pháp đại số hoặc phương pháp thử và sai.

Sử dụng phương pháp đại số:

Từ phương trình (1), ta có x = ? - y.

Thay x vào phương trình (2), ta có:

17(? - y) + 5y = 165

Simplifying the equation, we get:

17? - 17y + 5y = 165

Combining like terms, we get:

17? - 12y = 165

Rearranging the equation, we get:

17? = 165 + 12y

Dividing both sides by 17, we get:

? = (165 + 12y)/17

Since ? and y must be whole numbers, we can try different values of y to find the solution.

Let's start with y = 1:

? = (165 + 12(1))/17 = 177/17 ≈ 10.41

This is not a whole number, so y = 1 is not a valid solution.

Let's try y = 2:

? = (165 + 12(2))/17 = 189/17 ≈ 11.12

This is not a whole number, so y = 2 is not a valid solution.

Let's try y = 3:

? = (165 + 12(3))/17 = 201/17 ≈ 11.82

This is not a whole number, so y = 3 is not a valid solution.

Let's try y = 4:

? = (165 + 12(4))/17 = 213/17 ≈ 12.53

This is not a whole number, so y = 4 is not a valid solution.

Let's try y = 5:

? = (165 + 12(5))/17 = 225/17 ≈ 13.24

This is not a whole number, so y = 5 is not a valid solution.

Let's try y = 6:

? = (165 + 12(6))/17 = 237/17 ≈ 13.94

This is not a whole number, so y = 6 is not a valid solution.

Let's try y = 7:

? = (165 + 12(7))/17 = 249/17 ≈ 14.65

This is not a whole number, so y = 7 is not a valid solution.

Let's try y = 8:

? = (165 + 12(8))/17 = 261/17 ≈ 15.35

This is not a whole number, so y = 8 is not a valid solution.

Let's try y = 9:

? = (165 + 12(9))/17 = 273/17 ≈ 16.06

This is not a whole number, so y = 9 is not a valid solution.

Let's try y = 10:

? = (165 + 12(10))/17 = 285/17 ≈ 16.76

This is not a whole number, so y = 10 is not a valid solution.

Let's try y = 11:

? = (165 + 12(11))/17 = 297/17 ≈ 17.47

This is not a whole number, so y = 11 is not a valid solution.

Let's try y = 12:

? = (165 + 12(12))/17 = 309/17 ≈ 18.18

This is not a whole number, so y = 12 is not a valid solution.

Let's try y = 13:

? = (165 + 12(13))/17 = 321/17 ≈ 18.88

This is not a whole number, so y = 13 is not a valid solution.

Let's try y = 14:

? = (165 + 12(14))/17 = 333/17 ≈ 19.59

This is not a whole number, so y = 14 is not a valid solution.

Let's try y = 15:

? = (165 + 12(15))/17 = 345/17 ≈ 20.29

This is not a whole number, so y = 15 is not a valid solution.

Let's try y = 16:

? = (165 + 12(16))/17 = 357/17 ≈ 21

This is a whole number, so y = 16 is a valid solution.

Therefore, Mai's mother bought 16 pens and 16 notebooks for her.