In herd of X cattles,the ratio of number of bulls to cow is 1:6. Find the number of bulls in terms of X
If the ratio of the number of bulls to cows is 1:6, then we can write this as a fraction:
1/6.
To find the number of bulls, we'll set up a proportion using this ratio. Let B represent the number of bulls and C represent the number of cows.
B/C = 1/6
We know that the total number of cattles is equal to the sum of the number of bulls and cows:
B + C = X
Now we have a system of two equations:
B/C = 1/6
B + C = X
To solve for B in terms of X, we can isolate B in the second equation:
B = X - C
Substitute this expression for B in the first equation:
(X - C)/C = 1/6
To solve for C, we'll multiply both sides of the equation by 6C:
6(X - C) = C
Distribute on the left side:
6X - 6C = C
Add 6C to both sides:
6X = 7C
Divide both sides by 7:
(6/7)X = C
Now we have C in terms of X. To find B in terms of X, substitute this expression for C in the expression for B:
B = X - (6/7)X
B = (7/7)X - (6/7)X
B = (1/7)X
Therefore, the number of bulls in terms of X is (1/7)X.
Let's assume the number of bulls in the herd is "B" and the number of cows is "C". According to the given information, the ratio of bulls to cows is 1:6.
This ratio can be written as:
B/C = 1/6
To find the number of bulls in terms of X, we need to relate it to the total number of cattle (X).
We know that the total number of cattle is the sum of the number of bulls and the number of cows:
X = B + C
Since we have the ratio B/C = 1/6, we can substitute C in terms of B using this ratio:
C = 6B
Now we can substitute C in the equation X = B + C:
X = B + 6B
Simplifying this equation gives:
X = 7B
Therefore, the number of bulls in terms of X is B = X/7.