### 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 π¦ 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 π¦. Use the equation to find the weekly cost of feeding a dog, given that it costs 5 dollars per week to feed a cat.

Letβs start with the first question to write an equation connecting π₯ and π¦. Weβre 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. Weβre told that there are 65 cats in the rescue center. So, they must cost 65π₯ dollars.

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

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 45π¦ equals 685. Which gives us 65 times five plus 45π¦ equals 685. Working out 65 times five gives us 325 plus 45π¦ equals 685.

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