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,

Question

Fill in the blanks to make the statements true. 

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 and________

(c) The equation formed is _________

(d) The solution of the equation is ________

(e) The number of 1st prizes is the number of 2nd prizes are ________

Answer 1

Let 1^st prizes are x in numbers.

∴ 2nd prizes are 30 – x in numbers.

According to question,

2000(x) +1000 (30 – x) = 52000

⇒ 2000x + 30000 – 1000x = 52000

⇒ 1000x + 30000 – 52000

⇒ 1000x = 52000 – 30000

⇒ 1000x = 22000

⇒ x = 22000/1000 = 22

∴30 – x = 30 – 22 = 8.

(a) 30

(b) 2000x + 1000(30 – x)

(c) 1000x + 30000 = 52000

(d) x = 22

(e) 22, 8