Video: Creating and Using Linear Equations in More Than One Variable

A pet rescue center relies on donations to look after the cats and dogs. It costs $π‘₯ per week to feed a cat and $𝑦 per week to feed a dog. There are 65 cats and 45 dogs in the center, and the total weekly food bill for them is $685. Write an equation connecting π‘₯ and 𝑦. Use the equation to find the weekly cost of feeding a dog, given that it costs $5 per week to feed a cat.

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Video Transcript

A pet rescue center relies on donations to look after the cats and dogs. It costs π‘₯ dollars per week to feed a cat and 𝑦 dollars per week to feed a dog. There are 65 cats and 45 dogs in the center, and the total weekly food bill for them is 685 dollars. Write an equation connecting π‘₯ and 𝑦. Use the equation to find the weekly cost of feeding a dog, given that it costs 5 dollars per week to feed a cat.

Let’s start with the first question to write an equation connecting π‘₯ and 𝑦. We’re told that it costs π‘₯ dollars per week to feed a cat. So, for example, if we had two cats, then both of those costing π‘₯ dollars a week means that it would cost two π‘₯ dollars in total. Three cats would cost three π‘₯ dollars, and so on. We’re told that there are 65 cats in the rescue center. So, they must cost 65π‘₯ dollars.

We’re told that it costs 𝑦 dollars to feed a dog, so two dogs would be two 𝑦, 10 dogs would be 10𝑦. Therefore, for the 45 dogs in the center, this would cost 45𝑦 dollars. We’re told that the total weekly food bill for the cats and dogs is 685. So, 65π‘₯ plus 45𝑦 equals 685, which is our answer for the first question to write an equation connecting π‘₯ and 𝑦.

Looking at the second question, to use this equation to find the weekly cost of feeding a dog, given that it costs 5 dollars per week to feed a cat. This means that we now know that π‘₯ is equal to five. So, we substitute this into the equation 65π‘₯ plus 45𝑦 equals 685. Which gives us 65 times five plus 45𝑦 equals 685. Working out 65 times five gives us 325 plus 45𝑦 equals 685.

To find 45𝑦, we subtract 325 from both sides of the equation. Therefore, 45𝑦 is equal to 360. To find 𝑦, we do the inverse operation to multiplying by 45. So, we divide both sides by 45. So, 𝑦 equals eight. Since we know that 𝑦 was the cost of feeding a dog, then this will be our answer. So, we have 65π‘₯ plus 45𝑦 equals 685 for our first question and 8 dollars for the answer to our second question.

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