Question

A sum of $ 3000 is to be given in the form of 63 prizes. If the prize money is either $ 100 or $ 25. Find the number of prizes of each type.​

Answer 1

$\huge\mathfrak\blue{☃︎Answer☃︎}$

$\mathbb\purple{Solution}$

Let's take the sum of the number as = X

Let's take the prize as = Y

$\mathbb\red{Given:}$

Total amount = $3000

Total prize = 63

$\mathbb\orange{To find;}$

the number of prizes of each type = ??

$\mathbb\green{Now:}$

x + y = 63

y = 63 - x --------------(1)

100x + 25y = 3000 ------------(2)

Now equate (1) in (2)

100x + 25y = 3000

100x + 25 [ 63 - x ] = 3000

100x + 1575 - 25x = 3000

100x - 25x + 1575 = 3000

75x + 1575 = 3000

75x = 3000 - 1575

75x = 1425

x = 1425 / 75

x = 19 -------------------(3)

Now substitute (3) in (1)

Y = 63 - x

Y = 63 - 19

Y = 44

$\huge\mathfrak\red{Both Number are=19,44}$

Answer 2

☃︎Answer☃︎

Solution

Let's take the sum of the number as = X

Let's take the prize as = Y

Given:

Total amount = $3000

Total prize = 63

Tofind;

the number of prizes of each type = ??

Now:

x + y = 63

y = 63 - x --------------(1)

100x + 25y = 3000 ------------(2)

Now equate (1) in (2)

100x + 25y = 3000

100x + 25 [ 63 - x ] = 3000

100x + 1575 - 25x = 3000

100x - 25x + 1575 = 3000

75x + 1575 = 3000

75x = 3000 - 1575

75x = 1425

x = 1425 / 75

x = 19 -------------------(3)

Now substitute (3) in (1)

Y = 63 - x

Y = 63 - 19

Y = 44

$\huge\mathfrak\red{Both Number are=19,44}$