Question

Question 24

Fill in the blanks to make the statement true.
In a Mathematics quiz, 30 prizes consisting of 1st and 2nd prizes only are to be given. 1st and 2nd prizes are worth Rs. 2000 and Rs. 1000, respectively. If the total prize money is Rs. 52000, 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 ...........

Answer 1

Given, number of prizes = 30
Total prize money = Rs. 52000, 1st and 2nd prizes are worth Rs. 2000 and Rs. 1000, respectively.

(a) It 1st prizes are 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),
$\Rightarrow 2000x+30000-1000x=52000\Rightarrow 1000x+30000=52000$

(d) The solution of the equation is 22.
From (c), 1000x + 30000 = 52000
$\Rightarrow 1000x=52000-30000=22000\Rightarrow x=\frac{22000}{1000}=22$

(e) The number of 1st prizes are 22 and the number of 2nd prizes are 8.
From (b), 2000x + 1000(30 - x) = 52000
2x+ (30-x) = 52
x + 30 = 52
$\Rightarrow$ x = 52 - 30 = 22
$\therefore$ Number of 2nd prizes = 30 - 22 = 8.