MArgie is responsible for buying a weeks supply of food and medication for the dogs and cats at the local shelter.  The food and medication for dogs cost twice as much as those supplies for cats....

MArgie is responsible for buying a weeks supply of food and medication for the dogs and cats at the local shelter.  The food and medication for dogs cost 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 dogs food and medication. Set up a system and solve. Put answer in exact value form.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to come up with the following notations for the costs of food and medication for dogs and cats, such that:

x = cost of food and medication for each dog

y = cost of food and medication for each cat

The problem provides the information that the food and medication for dogs cost twice as much as those supplies for cats, hence, you need to set up the following equation, such that:

x = 2y

Since the budget is `$4,240` and there exists `24` dogs and `164` cats that Margie needs to feed, you can set up the second equation of the system, such that:

`24x + 164y = 4240`

Hence, you need to evaluate the following system of simultaneous equations, such that:

`{(x = 2y),(24x + 164y = 4240):}`

Replacing 2y for x in the bottom equations, yields:

`{(x = 2y),(24*2y + 164y = 4240):}`

`{(x = 2y),(48y + 164y = 4240):}`

`{(x = 2y),(212y = 4240):} => {(x = 2y),(y = 4240/212):} => {(x = 2y),(y = 20):} => {(x = 40),(y = 20):}`

Hence, evaluating the budget for medication and food for each dog and each cat yields that Margie can spend `$40` for each dog and `$20` for each cat.

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