Question

14. A sum of $2700 is to be given in the form of 63 prizes. If the prize is of

either $100 or $25, find the number of prizes of each type.

Answer 1

$100 prize = 15, $25 prize = 48

Explanation:

Let,

$100 prize = x

$25 prize = y

=> x + y = 63 (1)

=> 100x + 25y = 2700 (2)

=> 100x/25 + 25y/25 = 2700/25

=> 4x + y = 108 (3)

On subtracting 2 and 3

=> 4x + y - (x + y) = 108 - 63

=> 4x + y - x - y = 45

=> 3x = 45

=> x = 15

=> 15 + y = 63

=> y = 63 - 15

=> y = 48

Answer 2

• 15 at $100
• 48 at $25

Explanation:

Let x represent the number of higher-value ($100) prizes. Then (63-x) is the number of $25 prizes. The total value of the prizes is ...

100x +25(63 -x) = 2700

75x = 1125 . . . . . . . . . subtract 1575 and simplify

x = 15 . . . . . . . . . divide by 75; number of $100 prizes

63-x = 63 -15 = 48 . . . . number of $25 prizes

There are 15 $100 prizes and 48 $25 prizes.