A man bought a tray of eggs at shs. 300 per egg, on the way x eggs broke. He sold the remaining eggs at sh. 500 each and made a profit of sh. 3500. How many eggs did he sell?

Bei ya kununua yai moja = sh. 300
Bei ya kuuza yai moja = sh. 500
Jumla ya faida = sh. 3500

Acha $N_s$ iwe idadi ya mayai yaliyouzwa.
Acha $X$ iwe idadi ya mayai yaliyovunjika.
Acha $N_b$ iwe idadi ya mayai yaliyonunuliwa.

Jumla ya gharama (Total Cost, CP) = $N_b \times 300$
Jumla ya mapato (Total Revenue, SP) = $N_s \times 500$

Tunajua kuwa idadi ya mayai yaliyonunuliwa ni sawa na idadi ya mayai yaliyouzwa pamoja na yaliyovunjika:

Faida = Jumla ya Mapato - Jumla ya Gharama

Badilisha $N_b = N_s + X$ kwenye mlinganyo wa faida:

Gawanya mlinganyo mzima kwa 100 ili kurahisisha zaidi:

Panga upya mlinganyo ili kupata $N_s$:

Kwa kuwa $N_s$ lazima iwe namba kamili (idadi ya mayai), $35 + 3X$ lazima iwe namba shufwa (even number). Kwa sababu 35 ni namba witiri (odd number), $3X$ lazima iwe namba witiri ili jumla yao iwe shufwa. Hii inamaanisha $X$ lazima iwe namba witiri.

Katika matatizo kama haya ambapo thamani ya $X$ haijatolewa, tunachukua thamani ndogo zaidi ya $X$ inayowezekana ambayo inatoa jibu kamili.
Chagua $X = 1$.

Ikiwa $N_s = 19$ na $X = 1$:
Idadi ya mayai yaliyonunuliwa $N_b = N_s + X = 19 + 1 = 20$.
Jumla ya gharama = $20 \times \text{sh. } 300 = \text{sh. } 6000$.
Jumla ya mapato = $19 \times \text{sh. } 500 = \text{sh. } 9500$.
Faida = Jumla ya Mapato - Jumla ya Gharama = $\text{sh. } 9500 - \text{sh. } 6000 = \text{sh. } 3500$.
Faida hii inalingana na faida iliyotolewa kwenye swali.

Idadi ya mayai aliyouza ni: