Question

math a total of 80000 is to be distributed among 200 persons as prize a prize is either of 500 or 100 find the number of each prize​

Answer 1

Let x be the people who get 500 as cash prize and y be the people who get 100 as cash prize.

A total of 200 people are present,

$\sf{x + y = 200}..............(1)$

According to the question,

$\sf{500x + 100y = 80000} \\ \\ \implies \: \sf{5x + y = 800}...........(2)$

•From equation (1),

y=200-x

★Putting y=20-x in (2),we obtain:

5x+(200-x)=800

→4x=600

$\implies \: \huge{ \sf{x = 150}}$

★Putting x=60 in y=200-x,we obtain:

y=200-x

→y=200-150

$\implies \: \huge{\sf{y = 50}}$

Thus,people who get Rs.500 and Rs.100 as cash prize are 150 and 50 respectively

Answer 2

Step-by-step explanation:

Given:- Total number of persons =200

Total Prize money to be distributed = Rs 80,000

Let Number of Rs 500 prize distributed =x

Therefore, Number of Rs 200 prize distributed = (200 - x)

Now, Total prize money = Total Rs 500 money prize given to x person + Total Rs 100 money prize given to (200 - x) person

⇒ 500 x + (200 - x) 100 = 80000

⇒ 500 x + 20000 – 100 x =80000

⇒ 400 x = 80000 – 20000

⇒ x = 150

Therefore (200 - x)= 200 - 150 = 50 person got Rs 100 prize.

Hence 150 persons got Rs 500 prize money and 50 person got Rs 100 prize money.