Question

In a Mathematics quiz, 40 prizes consisting of 1st and 2nd prizes only are to be given. 1st and 2nd
prizes are worth `₹ 3000 and ₹ 2000, respectively. If the total prize money is ` ₹ 90,000 then
answer the following
(a) If 1st prizes are x in number ,find the number of 2nd prizes in terms of x
(b) Find the number of 1st prizes and the number of 2nd prizes .

Answer 1

Answer:

Given, number of prizes = 30

Total prize money = ₹52000, 1st and 2nd prizes are worth ₹2000 and ₹1000, respectively.

(a) 1st prize is x in number, the number of 2nd prizes are (30 – x), because total number of prizes are 30.

(b) Total value of prizes in terms of x are 2000x + 1000(30 – x)

(c) The equation formed is 1000x + 30000 = 52000

From (b), 2000x + 1000(30 – x) = 52000

⇒ 2000x + 30000 – 1000x = 54000

⇒ 1000x = 54000 – 30000

⇒ 1000x = 24000

(d) The solution of the equation is 22.

From (c), 1000x + 30000 = 52000.

⇒ 1000x = 52000 – 30000 = 22000

⇒ 1000x = 22000

⇒  

Step-by-step explanation: