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# 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 _____

**Solution:**

Let the numbers of 1^{st} prizes are x

Then the numbers of 2^{nd} prizes be (30 - x)

Now forming the equation, we get

2000(x) + 1000(30 - x) = 52000

2000x + 30000 - 1000x = 52000

1000x = 52000 - 30000

x = 22000/1000

x = 22

Hence, (30 - x) = 8

Thus,

(a) If 1st prizes are x in number the number of 2nd prizes are (30 - x).

(b) The total value of prizes in terms of x are 2000(x) + 1000(30 - x) or 1000x + 30000.

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

(d) The solution of the equation is 22.

(e) The number of 1st prizes are 22 and the number of 2nd prizes are 8.

**✦ Try This:** In a Mathematics quiz, 50 prizes consisting of 1st and 2nd prizes only are to be given. 1st and 2nd prizes are worth ₹ 1000 and ₹ 500, respectively. If the total prize money is ₹ 40000 then: (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 _____.

Let the numbers of 1^{st} prizes are x

Then the numbers of 2^{nd} prizes be (50 - x)

A/Q,

1000(x) + 500(50 - x) = 40000

1000x + 25000 - 500x = 40000

500x = 40000 - 25000

x = 15000/500

x = 30

Hence, (50 - x) = 20

Thus,

(a) If 1st prizes are x in number the number of 2nd prizes are (50 - x).

(b) The total value of prizes in terms of x are 1000(x) + 500(50 - x).

(c) The equation formed is 1000(x) + 500(50 - x) = 40000.

(d) The solution of the equation is 30.

(e) The number of 1st prizes are 30 and the number of 2nd prizes are 20.

**☛ Also Check: **NCERT Solutions for Class 7 Maths Chapter 4

**NCERT Exemplar Class 7 Maths Chapter 4 Problem 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 ____

**Summary:**

(a) If 1st prizes are x in number the number of 2nd prizes are 30, (b) The total value of prizes in terms of x are 2000(x) + 1000(30 - x) or 1000x + 30000, (c) The equation formed is 1000x + 30000 = 52000, (d) The solution of the equation is 22, (e) The number of 1st prizes are 22 and the number of 2nd prizes is 8

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