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A pet rescue center relies on donations to look after the cats and dogs.
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It costs π₯ dollars per week to feed a cat and π¦ dollars per week to feed a dog.
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There are 65 cats and 45 dogs in the center, and the total weekly food bill for them is 685 dollars.
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Write an equation connecting π₯ and π¦.
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Use the equation to find the weekly cost of feeding a dog, given that it costs 5 dollars per week to feed a cat.
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Letβs start with the first question to write an equation connecting π₯ and π¦.
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Weβre told that it costs π₯ dollars per week to feed a cat.
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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.
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Three cats would cost three π₯ dollars, and so on.
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Weβre told that there are 65 cats in the rescue center.
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So, they must cost 65π₯ dollars.
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Weβre told that it costs π¦ dollars to feed a dog, so two dogs would be two π¦, 10 dogs would be 10π¦.
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Therefore, for the 45 dogs in the center, this would cost 45π¦ dollars.
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Weβre told that the total weekly food bill for the cats and dogs is 685.
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So, 65π₯ plus 45π¦ equals 685, which is our answer for the first question to write an equation connecting π₯ and π¦.
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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.
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This means that we now know that π₯ is equal to five.
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So, we substitute this into the equation 65π₯ plus 45π¦ equals 685.
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Which gives us 65 times five plus 45π¦ equals 685.
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Working out 65 times five gives us 325 plus 45π¦ equals 685.
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To find 45π¦, we subtract 325 from both sides of the equation.
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Therefore, 45π¦ is equal to 360.
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To find π¦, we do the inverse operation to multiplying by 45.
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So, we divide both sides by 45.
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So, π¦ equals eight.
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Since we know that π¦ was the cost of feeding a dog, then this will be our answer.
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So, we have 65π₯ plus 45π¦ equals 685 for our first question and 8 dollars for the answer to our second question.