On a farm the number of chickens to the number of cows was in the ratio 5:3. The ratio became 3:2 after 300 chickens were sold. How many more chickens than cows were there at first?
if there are 5x chickens and 3x cows, then
(5x-300)/3x = 3/2
10x-600 = 9x
x = 600
so there were 2x = 1200 more chickens than cows
To solve this problem, let's break it down step by step:
Step 1: Let's assume the initial number of chickens and cows as 5x and 3x, respectively, where x is a constant representing the ratio.
Step 2: The ratio of chickens to cows is given as 5:3, so we have the equation 5x/3x.
Step 3: The ratio changes to 3:2 after 300 chickens are sold. This means the number of chickens becomes 5x - 300, and the number of cows remains the same, 3x.
Step 4: The new ratio is given as 3:2, so we have the equation (5x - 300)/(3x) = 3/2.
Step 5: Cross-multiplying, we get 2(5x - 300) = 3(3x).
Step 6: Expanding, we have 10x - 600 = 9x.
Step 7: Simplifying, we subtract 9x from both sides, which gives us x = 600.
Step 8: Now, we can substitute the value of x into the initial number of chickens and cows.
So, the initial number of chickens = 5x = 5 * 600 = 3000.
The initial number of cows = 3x = 3 * 600 = 1800.
Step 9: Finally, we can calculate the difference in the number of chickens and cows at first.
3000 - 1800 = 1200.
Therefore, there were 1200 more chickens than cows at first on the farm.