Answer:
There are 32 ferrets, 112 rabbits and 16 dogs at the shelter.
Step-by-step explanation:
There are 160 animals at the shelter. You know that of this amount of animals,[tex]\frac{1}{5}[/tex] are ferrets. So, the number of ferrets can be calculated by:
[tex]\frac{1}{5}*160[/tex]
To multiply a fraction by a whole number, any integer n can be written as the fraction [tex]\frac{n}{1}[/tex]. Then you multiply the numerators and denominators. In this case:
[tex]\frac{1}{5}*160=\frac{1}{5}*\frac{160}{1} =\frac{1*160}{5*1} =\frac{160}{5}[/tex]
Now you must reduce to the simplest form. To get a simplified result, divide the numerator by the denominator. In this case:
[tex]\frac{160}{5}[/tex] = 160 ÷ 5= 32
So, there are 32 ferrets at the shelter. Then, the number of animals remaining is calculated by the difference:
160 animals - 32 ferrets= 128 animals
[tex]\frac{7}{8}[/tex] of the remaining animals are rabbits. Then:
[tex]\frac{7}{8}*128[/tex]
Solving in the same way as in the previous case:
[tex]\frac{7}{8}*128=\frac{7}{8}*\frac{128}{1} =\frac{7*128}{8*1} =\frac{896}{8}[/tex]
[tex]\frac{896}{8}[/tex]= 896 ÷8= 112
So, there are 112 rabbits at the shelter. Then the remaining animals will be dogs, which will be calculated by the difference:
128 animals - 112 rabbits= 16
Finally, there are 16 dogs at the shelter.
