A merchant bought 50 animals, including goats and sheep. The cost is 28,000 rupees. The price of a goat and a sheep is Rs.500 and Rs.750 respectively but how many goats does that trader have?
How many sheep did he buy?
Answers
Answer:
The merchant bought 38 goats and 12 sheeps.
Step-by-step explanation:
Let the merchant buy 'x' goats and 'y' sheeps
Then, according to the Question,
Total animals = 50
x + y = 50
x = 50 - y ------- 1
Next,
Each goat costs Rs.500 and each sheep costs Rs.750, and it totally costs Rs.2800
So,
500x + 750y = 28000
Dividing the whole equation with 250 we get,
(500/250)x + (750/250)y = (28000/250)
2x + 3y = 112 ------- 2
Now, substituting eq.1 in eq.2 we get,
2(50 - y) + 3y = 112
100 - 2y + 3y = 112
3y - 2y = 112 - 100
y = 12 (sheeps)
Putting y = 12 in eq.1 we get,
x = 50 - 12
x = 38 (goats)
We can also check this,
Total animals = 50
38 + 12 = 50
50 = 50 (Correct)
Also,
500(38) + 750(12) = 28000
19000 + 9000 = 28000
28000 = 28000 (Correct)
Thus, it is correct.
Hence,
The merchant bought 38 goats and 12 sheeps.
Hope it helped and believing you understood it........All the best