Question

a sum of 3000 is to given in the of form of 63 prizes. if a prizes is of either 100or of 25 find the number of prizes of each type

Answer 1

Total prizes of ₹100 = x
Total prizes of ₹25 = y

Total prizes = 63
x + y = 63 ……(1)

Cost of total prizes = ₹3000
100x + 25y = 3000
Divide both sides by 25
4x + y = 120 ……(2)

(1) - (2)
x + y - 4x - y = 63 - 120
-3x = -57
x = 19

If x = 19 then Equation (1) becomes
19 + y = 63
y = 63 - 19
y = 44

∴ There are 19 prizes which cost ₹100 and 44 prizes which cost ₹25

Answer 2

Let the number of 100 prizes be x and 25 prizes be y
We can make 2 equations regarding number of prizes and total value
Solving them gives
Number of 100 prizes are 19 and 25 prizes are 44