A student bought some maths books and some computing books at a bookstore for K230. The maths books cost K15 each and the computing books cost K25 each. If he bought 12 books, how many of each type books did he buy? (4 marks)

Let $m$ be the number of maths books.
Let $c$ be the number of computing books.

From the problem, we have two pieces of information that can be translated into equations:

1. The total number of books bought is 12. $$m + c = 12 \quad (1)$$
2. The total cost of the books is K230. Maths books cost K15 each, and computing books cost K25 each. $$15m + 25c = 230 \quad (2)$$

From equation (1), express $m$ in terms of $c$:

$$m = 12 - c \quad (3)$$

Substitute this expression for $m$ into equation (2):

$$15(12 - c) + 25c = 230$$

Distribute the 15:

$$180 - 15c + 25c = 230$$

Combine the terms with $c$:

$$180 + 10c = 230$$

Subtract 180 from both sides:

$$10c = 230 - 180$$ $$10c = 50$$

Divide by 10 to find $c$:

$$c = \frac{50}{10}$$ $$c = 5$$

$$m = 12 - c$$ $$m = 12 - 5$$ $$m = 7$$

The student bought 7 maths books and 5 computing books.

The student bought:

• 7 maths books
• 5 computing books