Let’s assume the weights of the cat, rabbit, and dog are represented by the variables C, R, and D respectively.
From the given information, we can set up a system of equations:
C + R = 10 (Cat and Rabbit weigh 10kg together)
D + R = 20 (Dog and Rabbit weigh 20kg together)
C + D = 24 (Cat and Dog weigh 24kg together)
We can solve this system of equations to find the values of C, R, and D.
From equation 1, we can isolate C: C = 10 - R
From equation 2, we can isolate D: D = 20 - R
Now substitute these expressions for C and D into equation 3:
(10 - R) + (20 - R) = 24
Combine like terms:
30 - 2R = 24
Subtract 30 from both sides:
-2R = -6
Divide by -2:
R = 3
Now that we have the weight of the rabbit (R = 3 kg), we can substitute it back into equations 1 and 2 to find the weights of the cat and the dog:
From equation 1: C = 10 - R = 10 - 3 = 7 kg
From equation 2: D = 20 - R = 20 - 3 = 17 kg
So, the weights of the cat, rabbit, and dog are C = 7 kg, R = 3 kg, and D = 17 kg.
Finally, to find the total weight of all three animals together:
Total weight = C + R + D = 7 + 3 + 17 = 27 kg
Therefore, the total weight of the cat, rabbit, and dog together is 27 kg.