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Ruby spends three dollars and eighty-eight cents every day on transportation to and from work.
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Write a function rule that relates the total amount of money Ruby spends on transportation to the number of Ruby’s working days.
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Let 𝑥 represent the number of working days and 𝑦 the total amount of money she spends on transportation.
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We need to write a function rule.
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Our function rule will have an 𝑥 that represents the number of working days and a 𝑦 that represents the total amount of money Ruby spends on transportation.
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We can think of our function rule like a machine; you input some information that you know, the function rule occurs, and then it gives you some kind of output.
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In our case, we’ll input the number of working days; these are the days that Ruby uses the transportation.
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After the function rule occurs in our machine, it will output the total amount spent on transportation for those working days.
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The question is what happens here.
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What happens inside the function rule in our problem?
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How do we go from the working days to the total money spent?
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And this is the key.
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The key is the three dollars and eighty-eight cents Ruby spends on her working days.
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Our function rule is the number of working days multiplied by three dollars and eighty-eight cents and that gives us the total that Ruby spent.
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Our problem wants us to use 𝑥 to represent the number of working days and 𝑦 to represent the total amount of money.
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So we substitute 𝑥 and 𝑦, respectively, for the working days and the total amount.
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Simplifying it a little bit, three dollars and eighty-eight cents times 𝑥 equals 𝑦.
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Using this function rule, we’ll always be able to find out the total amount of money that Ruby spends on transportation if we know 𝑥 — how many days she worked.