24. In a Mathematics quiz, 30 prizes consisting of 1st and 2nd prizes only are to be given. 1st and 2nd prizes are worth ₹2000 and ₹1000, respectively. If the total prize money is ₹52,000 then show that:
(a) If 1st prizes are x in number the number of 2nd prizes are ________.
(b) The total value of prizes in terms of x are ________.
(c) The equation formed is ________.
(d) The solution of the equation is ________.
(e) The number of 1st prizes are ________ and the number of 2nd prizes are ________.
(a) 30 − x
(b) 2000x + 1000(30 − x)
(c) 1000x + 30000 = 52000
(d) 22
(e) 22, 8
Total value = 2000x + 1000(30 − x). Equation = 1000x + 30000 = 52000 ⇒ x = 22. So 1st = 22, 2nd = 8.