the cost of 6 cows are same as cost of 8 goats. if cost of 9 cows and twice numbered goats is rs. 9000, then find the cost of 3 cows and 6 goats?
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not sure what you mean by
"9 cows and twice numbered goats"
twice what number?
To find the cost of 3 cows and 6 goats, we need to determine the individual costs of cows and goats.
Let's assign variables to represent the cost of a cow and a goat. Let's say the cost of a cow is 'C' and the cost of a goat is 'G'.
According to the given information, the cost of 6 cows is the same as the cost of 8 goats. This can be written as:
6C = 8G ---(Equation 1)
We're also given that the cost of 9 cows and twice the number of goats is Rs. 9000. Mathematically, this can be expressed as:
9C + 2(8G) = 9000 ---(Equation 2)
Now, we have two equations with two variables. We can solve these equations simultaneously to find the values of 'C' and 'G'.
First, let's simplify Equation 2 by distributing the multiplication:
9C + 16G = 9000 ---(Equation 3)
Now, we have two equations:
6C = 8G ---(Equation 1)
9C + 16G = 9000 ---(Equation 3)
There are multiple methods to solve these equations, such as substitution or elimination. Let's use substitution to solve for 'C' and 'G'.
From Equation 1, we can express 'G' in terms of 'C':
G = (6C) / 8 ---(Equation 4)
Now, substitute this value of 'G' into Equation 3:
9C + 16((6C) / 8) = 9000
Simplify further:
9C + 6C = 9000
Combining like terms:
15C = 9000
Divide both sides by 15:
C = 600
Now, substitute the value of 'C' back into Equation 1 to find 'G':
6C = 8G
6(600) = 8G
3600 = 8G
G = 450
So, the cost of a cow is Rs. 600 and the cost of a goat is Rs. 450.
To find the cost of 3 cows and 6 goats, we multiply the respective costs by the number of cows and goats:
Cost of 3 cows = 3 * 600 = Rs. 1800
Cost of 6 goats = 6 * 450 = Rs. 2700
Therefore, the cost of 3 cows and 6 goats is Rs. 1800 + Rs. 2700 = Rs. 4500.