The average weight of goats and sheep in a shelter is 65 kgs, the ratio of goat to sheep is 2:1 and the total weight of sheep is 207 kgs less than the total weight of goats, then what is the total number of goat and sheep in the shelter
Answers
Answer:
Multiple answers possible
Sheeps 3 9 23 69 207
Goats 6 18 46 138 414
Step-by-step explanation:
the ratio of goat to sheep is 2:1
Let say Number of Sheep = K
=> number of Goat = 2K
Average Weight of Sheep = S
total Weight of Sheep = SK
Total Weight of Goats = SK + 207
Total Weight = SK + SK + 207 = 2SK + 207
Total Goat + Sheeps = 3K
Average weight = 65 kg
=> 65 * 3K = 2SK + 207
=> 195K = 2SK + 207
=> k(195 - 2S) = 207
=> K = 207/(195 - 2S)
K is an ineteger
207 = 3 * 3 * 23
K can be 3 , 9 , 23 , 69 , 207
=> 195 - 2S can be 1 , 3 , 9 , 23 , 69
Using K = 207 , 195 - 2S = 1 => S = 97
Sheeps = 207 , Goat = 414
Using K = 69 , 195 - 2S = 3 => S = 96
Sheeps = 69 , Goat = 138
Using K = 23 , 195 - 2S = 9 => S = 93
Sheeps = 23 , Goat = 46
Using K = 9 , 195 - 2S = 23 => S = 86
Sheeps = 9 , Goat = 18
Using K = 3 , 195 - 2S = 69 => S = 63
Sheeps = 3 , Goat = 6
Sheeps 3 9 23 69 207
Goats 6 18 46 138 414
Verification for each cae given below
Number Averagae wt Total wt
Sheeps 207 97 20079
Goats 414 49 20286
621 65 40365
Number Averagae wt Total wt
Sheeps 69 96 6624
Goats 138 49.5 6831
207 65 13455
Number Averagae wt Total wt
Sheeps 23 93 2139
Goats 46 51 2346
69 65 4485
Number Averagae wt Total wt
Sheeps 9 86 774
Goats 18 54.5 981
27 65 1755
Number Averagae wt Total wt
Sheeps 3 63 189
Goats 6 66 396
9 65 585