Question

A sum of $2700 is to be given in the form of 63 prizes. If the prize is of either $100 and $25, find the number of prize of each type.

Answer 1

$\huge\underbrace\pink{\dag Final Answer \dag}$

there are 15 prizes for Rs. 100 and 48 prizes for Rs. 25

$\huge\underbrace\purple{\dag Solution \dag}$

Since we have given that

Number of prizes = 63

Prize amount = Rs. 2700

Prize value can be of Rs. 100 or Rs.25

Let the number of prizes for Rs. 100 be 'x'.

Let the number of prizes for Rs. 25 be '63-x'.

According to question, we get

$100x + 25(63 - x) = 2700 \\ 100x + 1575 - 25x = 2700 \\ 75 x= 2700 - 1575 \\ 75x = 1125 \\ x = \frac{1125}{75} \\ x = 15$

So, Number of prizes for Rs. 25 would be

$63 - 15 = 48$

Hence, there are 15 prizes for Rs. 100 and 48 prizes for Rs. 25.