Two families, A and B bought oranges, mangoes and bananas in two weeks as shown in the following tables. (a) Form matrices to represent the information provided. (b) Determine the total number of fruits of each type bought by each family.

here are the solutions to the problems:

Unnumbered Problem (System of Equations):
The given system of equations is:

1. $4b + 3p = 315$
2. $8b + 2p = 530$

Step 1: Multiply equation (1) by 2 to eliminate $b$.

$$2(4b + 3p) = 2(315)$$ $$8b + 6p = 630 \quad \text{(Equation 3)}$$

Step 2: Subtract equation (2) from equation (3).

$$(8b + 6p) - (8b + 2p) = 630 - 530$$ $$4p = 100$$

Step 3: Solve for $p$.

$$p = \frac{100}{4}$$ $$p = 25$$

Step 4: Substitute the value of $p$ into equation (1).

$$4b + 3(25) = 315$$ $$4b + 75 = 315$$ $$4b = 315 - 75$$ $$4b = 240$$

Step 5: Solve for $b$.

$$b = \frac{240}{4}$$ $$b = 60$$

The cost of a book is Ksh 60 and the cost of a pen is Ksh 25.
The final answer is $\boxed{\text{Book: Ksh 60, Pen: Ksh 25}}$.