a pet shop owner had an equal number of hamster and puppies for sale. the hamster were put equally int o 4 cages and the puppies were put equally into 12 cages. at the end of the day, he had sold 3 cages of hamsters and 6 cages of puppies. if the total number of animals sold was 30, how many hamsters and how many puppies were sold?
To solve this problem, let's break down the information and try to find a solution step by step.
Let's assume the number of hamsters and puppies as 'x.'
According to the problem, the number of hamsters and puppies for sale is equal, so we can write the equation: Number of Hamsters = Number of Puppies = x.
The hamsters were put equally into 4 cages, meaning there were x/4 hamsters in each cage.
Similarly, the puppies were put equally into 12 cages, so there were x/12 puppies in each cage.
At the end of the day, the pet shop owner sold 3 cages of hamsters and 6 cages of puppies. Since each cage contains x/4 hamsters and x/12 puppies, we can calculate the total number of animals sold:
Number of Hamsters Sold = 3 * (x/4), as there are x/4 hamsters in each cage and 3 cages were sold.
Number of Puppies Sold = 6 * (x/12), as there are x/12 puppies in each cage and 6 cages were sold.
We are given that the total number of animals sold is 30, so we can write the equation:
Number of Hamsters Sold + Number of Puppies Sold = 30.
Substituting the above calculations into the equation:
3*(x/4) + 6*(x/12) = 30.
Now, let's solve this equation to find the value of x, which represents the number of hamsters and puppies.
Multiplying through by 12 to eliminate the fractions:
3x + 2x = 360.
Combining like terms:
5x = 360.
Dividing both sides by 5:
x = 72.
Therefore, there were 72 hamsters and 72 puppies initially.
To find the number of animals sold:
Number of Hamsters Sold = 3 * (72/4) = 3 * 18 = 54.
Number of Puppies Sold = 6 * (72/12) = 6 * 6 = 36.
So, the number of hamsters sold is 54, and the number of puppies sold is 36.