In a class, the total number of boys to girls is 60. 1/4 of the number of boys exceeds the number of girls by 8. Find the number of boys and girls.

Wacha $b$ iwe idadi ya wavulana na $g$ iwe idadi ya wasichana.
Kutoka taarifa ya kwanza: Jumla ya wavulana na wasichana ni 60.

$$b + g = 60 \quad \text{(Mlinganyo 1)}$$

Kutoka taarifa ya pili: Idadi ya wavulana inazidi idadi ya wasichana kwa 8.

$$b = g + 8 \quad \text{(Mlinganyo 2)}$$

Badilisha $b$ katika Mlinganyo 1 na $g + 8$:

$$(g + 8) + g = 60$$

Unganisha $g$ na utatue:

$$2g + 8 = 60$$ $$2g = 60 - 8$$ $$2g = 52$$ $$g = \frac{52}{2}$$ $$g = 26$$

Tumia thamani ya $g = 26$ katika Mlinganyo 2:

$$b = g + 8$$ $$b = 26 + 8$$ $$b = 34$$

Idadi ya wavulana ni 34 na idadi ya wasichana ni 26.

Idadi ya wavulana ni: $\boxed{34}$
Idadi ya wasichana ni: $\boxed{26}$