The ratio of cows to pigs to chickens on a farm was 15:14:12. Half of the chickens were sold to another farm, and then there were 56 more pigs than chickens. How many animals were on the farm in the beginning? how many chickens were sold?
p/c = 14/12 so p =14c/12 = =7c/6
p - c/2 = 56
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7c/6 - 3 c/6 = 56
4 c/6 = 56
c/6 = 14
c = 84 (and 42 were sold)
p = 7 c/6 = 98
cows = 5 c/4 = 105
84+98+105
check my arithmetic !
257 all in all. Thank you so much Damon
You are welcome.
To solve this problem, let's break it down into smaller steps:
Step 1: Calculate the number of chickens sold.
- We are given that half of the chickens were sold, which can be represented as 1/2.
- Let's assume the number of chickens on the farm initially is 12x (since the ratio of chickens is 15:14:12).
- Therefore, the number of chickens sold is (1/2) * 12x = 6x.
Step 2: Calculate the number of pigs.
- We are given that there were 56 more pigs than chickens.
- Since the number of pigs is given as a ratio of 14, we can express it as 14x.
- The number of chickens is 12x, so we can express the number of pigs as 14x - 12x = 2x.
Step 3: Calculate the number of cows.
- The ratio of cows to pigs to chickens is given as 15:14:12.
- Since we already know the number of chickens (12x) and pigs (2x), we can calculate the number of cows as 15x.
Step 4: Calculate the total number of animals on the farm initially.
- The total number of animals on the farm initially is the sum of cows, pigs, and chickens.
- Total animals = number of cows + number of pigs + number of chickens.
- Total animals = 15x + 2x + 12x = 29x.
Therefore, the total number of animals on the farm initially is 29x.
To determine the exact number of animals on the farm, we would need to know the value of x.