The weight of Meg's dog is 2 1/2 times more than that of her cat. If both animals weight 42 lbs, find the weight of each animal?Please show your work.
Let c = the weight of the cat.
c + 2.5c = 42
3.5c = 42
c = 12
To find the weight of Meg's dog and cat, let's assume the weight of the cat is x lbs.
According to the information given, the weight of the dog is 2 1/2 times more than the cat's weight, which means the dog weighs x + 2 1/2x lbs.
We know that the combined weight of the dog and cat is 42 lbs, so we can set up the equation:
x + (x + 2 1/2x) = 42
To solve this equation, we need to first simplify it.
x + x + 2 1/2x = 42
Combining like terms:
4 1/2x = 42
Now, let's convert the mixed fraction to an improper fraction:
9/2x = 42
To isolate x, we need to divide both sides of this equation by 9/2:
(9/2x)/(9/2) = 42/(9/2)
Simplifying the equation further:
1x = (42 * 2)/9
1x = 84/9
Now, let's divide:
x = 9 1/3
Therefore, the weight of the cat is approximately 9 1/3 lbs.
To find the weight of the dog, we can substitute the weight of the cat, x, into the equation:
x + 2 1/2x = dog's weight
(9 1/3) + 2 1/2(9 1/3) = dog's weight
To simplify this equation, let's first convert the mixed fractions to improper fractions:
(28/3) + 2 1/2 (28/3) = dog's weight
Now, let's add:
(28/3) + (14/3) = dog's weight
42/3 = dog's weight
14 = dog's weight
Therefore, the weight of the dog is approximately 14 lbs.