Q5b. For his Christmas gift little Kofi was taken to a stationary store. For one pencil and two erasers he paid 14 Leones. Two pencils and three erasers cost him 24 Leones. How much does each pencil and each eraser cost.

The formula for the $n$-th term of an Arithmetic Progression (A.P.) is $a_n = a + (n-1)d$, where $a$ is the first term and $d$ is the common difference.
Given $a_5 = -12$:

$$a + (5-1)d = -12$$ $$a + 4d = -12 \quad (*)$$

Given $a_{10} = -27$:

$$a + (10-1)d = -27$$ $$a + 9d = -27 \quad (**)$$

Subtract equation $(*)$ from equation $(**)$:

$$(a + 9d) - (a + 4d) = -27 - (-12)$$ $$5d = -27 + 12$$ $$5d = -15$$ $$d = \frac{-15}{5}$$ $$d = -3$$

$$a + 4(-3) = -12$$ $$a - 12 = -12$$ $$a = -12 + 12$$ $$a = 0$$

The first term is $a=0$ and the common difference is $d=-3$.
The A.P. is $a, a+d, a+2d, \dots$

$$0, 0+(-3), 0+2(-3), \dots$$ $$0, -3, -6, \dots$$

Using the formula $a_n = a + (n-1)d$:

$$a_{15} = 0 + (15-1)(-3)$$ $$a_{15} = 0 + (14)(-3)$$ $$a_{15} = -42$$

The A.P. is $\boxed{0, -3, -6, \dots}$ and its 15th term is $\boxed{-42}$.