Theory question 102
Linear and Simultaneous EquationsIn a football match, the tickets for children and adults were sold at D 3.00 and D 5.00 respectively. If 400 people attended the football match and D1,700.00 was collected in ticket sales:
(a) how many tickets were sold to adults?
(b) Mr. Sonko sold 250 tickets. If 175 of the tickets were for adults, how much sales did he make altogether?
Show the model answer
Model answer
(a) Let c = children's tickets, a = adults' tickets: c + a = 400 and 3c + 5a = 1700
3(400 − a) + 5a = 1700 ⇒ 2a = 500 ⇒ a = 250 adults' tickets
(b) Children's tickets = 250 − 175 = 75
Sales = 175 × D5 + 75 × D3 = D875 + D225 = D1,100.00
Explanation
Form two simultaneous equations: one for people, one for money.