Margie is responsible for buying a week's supply of food and medication for the dogs and cats at the local shelter. The food and medication for dogs costs twice as much as those supplies for cats. She needs to feed 164 cats and 24 dogs. Her budget is $4,240. How much can Margie spend on each dog's food and medication. Set up a system and solve. Put answer in exact value form.

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Let c = the food and medication costs for cats in one week

Let d = the food and medication costs for dogs in one week

The food and medication for dogs costs twice as much as those supplied for cats: d = 2*c

There are 164 cats and 24 dogs.

In order to determine the cost of food and medication for all of the animals in the shelter you must multiply the cost per cat to the number of cats and add this to the cost per dog multiplied by the number of dogs:

164*c + 24*d = Cost

There is a maximum of $4,240 available therefore:

164*c + 24*d = 4240

Therefore the two equations required to solve this problem are:

d = 2*c

164*c + 24*d = 4240

First substitute the first equation into the second equation:

164*c + 24*2*c = 4240

Next simplify the equation and solve for c:

164*c + 48*c = 4240

212*c = 4240

c = 4240/212 = $20

Finally, substitute this value into the first equation:

d = 2*20 = $40

Therefore, Margie can spend $40/dog on food and medication for a week.

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