Question

A total of $10000 is distributed among 150 persons as gift. A gift is either of $50 or $100. Find the number of gifts of each type.

Answer 1

Answer:

Step-by-step explanation:

Total number of gifts = 150  

Let the number of $50 is x

Then the number of gifts of $100 is (150 - x)  

Amount spent on x gifts of $50 = $ 50x

Amount spent on (150 - x) gifts of $100 = $100(150 - x)  

Total amount spent for prizes = $10000

According to the question,  

50x + 100 (150 - x) = 10000  

⇒ 50x + 15000 - 100x = 10000

⇒ -50x = 10000 - 15000

⇒ -50x = -5000  

⇒ x = 5000/50

⇒ x = 100

⇒ 150 - x = 150 - 100 = 50

Therefore, gifts of $50 are 100 and gifts of $100 are 50.  

Answer 2

Answer:

Step-by-step explanation:

Let the no of gifts of $50=x

Let the no of gifts of $100=y

x+y=150

50x+100y=10000

By elimination method,

x+ y =150. (1)

50x+100y=10000. (2)

Multiply (1) by 50

50x+50y=7500. (3)

Subtract (2) from (3)

50x +50y = 7500

50x. +100y= 10000

-. -. -

________________

-50y=-2500

y=50

Put the value of yin (1)

x+y=150

x+50=150

x=100

Therefore, x=100, y=50