This question is essentially a question on linear equations. We have the following equation

Mrs Chan’s original money = $11 * x + $ 4 = $8 * (x + 5) + $3

Using the laws of arithmetic (distributivity of multiplication over addition), this gives us:

Mrs Chan’s original money = $(11x + 4) = $ (8x + 8*5 +3) = $(8x + 43)

We want to solve for x. Hence, we have apply laws of arithmetic:

11x + 4 = 8x + 43 => (11x + 4) – 8x = (8x + 43) – 8x =>

(3x + 4) = 43 => (3x +4) – 4 = 43 – 4 => 3x = 39 => (3x)/3 = 39/3 =>

x = 13.

Original Money = $(11x + 4) = $ (11*13+4) = $ (143+4) = $147.

let y be the max. amount of bowls she can buy. Then, ($147 – $6x) // $(x+5) = y 

Substituting x = 13, we have 69//18 = y.

y = 3 (because 4 * 18 = 72 > 69).

For part iii), it should be:
[147 – (6 × 11)] / 8 = y.
y = 10.125 ≈ 10

The variable “x” found in part b refers to the quantity of the plates and not the cost. Since the question told us clearly that she bought 6 plates, it is no longer a variable so it wouldn’t make sense to substitute x with another value again.

oops, thank you for the correction. I made a mistake with the equation. The right answer will be:

$147 – $11 * 6 (plates) // $8 = y

Hence, y = 81 // 8 = 10