If a cat is 4 times lighter than a dog and together they weigh 30 kg, how much does the cat weigh? - briefly
To determine the weight of the cat, we start by defining the variables. Let ( C ) represent the weight of the cat and ( D ) represent the weight of the dog. Given that the cat is 4 times lighter than the dog, we can express this relationship as ( D = 4C ).
The total weight of the cat and the dog together is 30 kg. Therefore, we can write the equation: ( C + D = 30 ).
Substituting ( D ) from the first equation into the second equation, we get: ( C + 4C = 30 ).
Simplifying this, we have: ( 5C = 30 ).
Solving for ( C ), we find: ( C = 30 / 5 = 6 ).
The cat weighs 6 kg.
If a cat is 4 times lighter than a dog and together they weigh 30 kg, how much does the cat weigh? - in detail
To determine the weight of the cat, we need to establish the relationship between the weights of the cat and the dog. Given that the cat is four times lighter than the dog, we can express this relationship mathematically. Let ( C ) represent the weight of the cat and ( D ) represent the weight of the dog. The information provided tells us that ( C = \frac{1}{4}D ).
Next, we know that the combined weight of the cat and the dog is 30 kg. This can be written as: [ C + D = 30 ]
Substituting ( C ) with ( \frac{1}{4}D ) in the equation, we get: [ \frac{1}{4}D + D = 30 ]
To solve for ( D ), we combine like terms: [ \frac{1}{4}D + \frac{4}{4}D = 30 ] [ \frac{5}{4}D = 30 ]
Multiplying both sides of the equation by ( \frac{4}{5} ) to isolate ( D ), we get: [ D = 30 \times \frac{4}{5} ] [ D = 24 ]
Now that we have the weight of the dog, we can find the weight of the cat. Since ( C = \frac{1}{4}D ), substituting ( D ) with 24 kg, we get: [ C = \frac{1}{4} \times 24 ] [ C = 6 ]
Therefore, the cat weighs 6 kg. This detailed approach ensures that we accurately determine the weight of the cat based on the given information and the established relationship between the weights of the cat and the dog.