A cat is 4 times lighter than a dog, and together they weigh 30 kilograms - how much does the cat weigh? - briefly
To determine the weight of the cat, we first need to establish the total combined weight of both animals, which is given as 30 kilograms. Since the cat is four times lighter than the dog, we can set up an equation where the weight of the cat is represented as ( C ) and the weight of the dog as ( D ). The relationship between their weights can be expressed as ( C = \frac{D}{4} ), and together they weigh 30 kilograms, so ( C + D = 30 ).
Substituting ( C = \frac{D}{4} ) into the equation ( C + D = 30 ), we get ( \frac{D}{4} + D = 30 ). Simplifying this, we have ( \frac{5D}{4} = 30 ). Solving for ( D ), we find ( D = 24 ) kilograms. Therefore, the weight of the cat is ( C = \frac{24}{4} = 6 ) kilograms.
A cat is 4 times lighter than a dog, and together they weigh 30 kilograms - how much does the cat weigh? - in detail
To determine the weight of the cat given that it is four times lighter than the dog and their combined weight is 30 kilograms, we need to follow a systematic approach involving algebraic equations.
Firstly, let's denote the weight of the dog as (D) and the weight of the cat as (C). According to the problem statement:
- The cat is four times lighter than the dog: (C = \frac{1}{4}D).
- Together they weigh 30 kilograms: (C + D = 30).
Now, we can substitute the first equation into the second to solve for one of the variables. Replacing (C) with (\frac{1}{4}D) in the second equation yields: [ \frac{1}{4}D + D = 30 ] Combining like terms, we get: [ \frac{5}{4}D = 30 ] To find (D), multiply both sides of the equation by (\frac{4}{5}): [ D = 30 \times \frac{4}{5} = 24 ] Now that we have the weight of the dog, we can determine the weight of the cat using the first equation: [ C = \frac{1}{4} \times 24 = 6 ] Therefore, the cat weighs 6 kilograms. This solution demonstrates how to apply basic algebraic principles to solve real-world problems involving weight comparisons and total weights.