Fill in the blanks to make the statements true. In a Mathematics quiz

1.	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» 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

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»

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)

(d) x = 22

(e) 22, 8