The pie chart below shows Lewis' expenditure for the month of November. Use it to answer the questions that follow. (a) Find the value of y. (b) If he spends sh. 36,000 on transport, calculate his monthly expenditure.

Kutokana na muundo wa chati, sekta za "food" na "rent" zinaunda nusu ya duara ya juu. Hivyo, jumla ya pembe zao ni $180^\circ$.

$$(3y + 30)^\circ + (2y + 40)^\circ = 180^\circ$$

Unganisha vigezo vya $y$ na namba:

$$(3y + 2y) + (30 + 40) = 180$$ $$5y + 70 = 180$$

Toa 70 kutoka pande zote mbili:

$$5y = 180 - 70$$ $$5y = 110$$

Gawanya kwa 5:

$$y = \frac{110}{5}$$ $$y = 22$$

Thamani ya $y$ ni 22.

$$\boxed{y = 22}$$

Swali la 32 (b): Ikiwa anatumia sh. 36,000 kwa usafiri, hesabu matumizi yake ya kila mwezi.

Pembe ya usafiri ni $(y + 50)^\circ$. Tumia thamani ya $y = 22$ kutoka sehemu (a).

$$\text{Pembe ya usafiri} = (22 + 50)^\circ = 72^\circ$$

Tunajua kuwa $72^\circ$ inawakilisha sh. 36,000. Jumla ya matumizi ya kila mwezi inawakilishwa na $360^\circ$.
Acha $E$ iwe jumla ya matumizi ya kila mwezi.

$$\frac{\text{Matumizi ya usafiri}}{\text{Jumla ya matumizi}} = \frac{\text{Pembe ya usafiri}}{\text{Jumla ya pembe}}$$ $$\frac{36,000}{E} = \frac{72^\circ}{360^\circ}$$

$$E = 36,000 \times \frac{360}{72}$$

Rahisisha sehemu $\frac{360}{72}$:

$$\frac{360}{72} = 5$$

Hivyo:

$$E = 36,000 \times 5$$ $$E = 180,000$$

Matumizi yake ya kila mwezi ni sh. 180,000.

$$\boxed{\text{sh. } 180,000}$$