In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 20 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter? Choose the correct choice from the following options
A) 75  B) 25  C) 30  D) 45  E) 60
This ratio question can be solved in a couple of different ways. Here's an Algebraic approach...   We're told that the ratio of the number of dogs to the number of cats is 15:7. We're then told that 20 more cats are added to this group and the ratio becomes 15:11. We're asked for the number of dogs.   Algebraically, since the number of dogs is a multiple of 15 and the number of cats is a multiple of 7, we can write this initial relationship as...   15X/7X   When we add the 20 cats and factor in the 'ending ratio', we have an equation....   15X/(7X+20) = 15/11   Here we have 1 variable and 1 equation, so we can solve for X....   (15X)(11) = (7X+20)(15)   (X)(11) = (7X+20)(1)   11X = 7X + 20   4X = 20   X = 5   With this X, we can figure out the initial number of dogs and cats...   Initial dogs = 15X = 15(5) = 75   Final 75nswer: 75
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In a certain animal shelter, the ratio of the number of dogs to the number of cats is 15 to 7. If 20 additional cats were to be taken in by the shelter, the ratio of the number of dogs to the number of cats would be 15 to 11. How many dogs are in the shelter?