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Amelia is making brooches to sell at a craft fair.
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It takes her five minutes to make a star brooch and seven minutes to make a bow brooch.
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On Saturday, she spent four and three-fourths hours making brooches.
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She made three fewer star brooches than bow brooches.
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Write an equation that can be used to find š¯‘¦, the number of star brooches that Amelia made.
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So in the question, we talk about two things: the amount of time it takes to make a brooch and how many brooches were made.
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Letā€™s first write an equation in terms of time.
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It takes her five minutes to make a star brooch.
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So we need to take the number of star brooches and multiply it by five.
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Next, it says it takes her seven minutes to make a bow brooch.
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So we will be adding these together so that way we know how much time was spent.
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It says, on Saturday, she spent four and three-fourths hour making brooches.
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However, thereā€™s something wrong with this equation.
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The five and the seven are in terms of minutes, and four and three-fourths is in number of hours.
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So letā€™s go ahead and change the four and three-fourths to minutes.
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That way, the entire equation is the same.
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There are 60 minutes in one hour.
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So if we have four hours, we need to take 60 and multiply it by four, so thatā€™s 240.
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But then we also have three-fourths of an hour, and 60 times three-fourths is 45.
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So four and three-fourths hours must be equal to 240 minutes plus 45 minutes, which is 285 minutes.
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Now we can begin talking about the number of brooches made.
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She made three fewer star brooches than bow brooches.
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And weā€™re to use š¯‘¦ to represent the number of star brooches.
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So again, she made three fewer star brooches than bow brooches.
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So there were less star brooches.
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So in order to find the number of star brooches, we would have to take the number of bow brooches and subtract three.
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So we know that star brooches can be represented by š¯‘¦.
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However, we need to know how to represent the number of bow brooches, and we need it to be in terms of š¯‘¦.
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So we have the equation that star equals bow minus three.
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So replace star with š¯‘¦ and solve for bow.
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So we need to add three to both sides of the equation.
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So the number of bow brooches is equal to š¯‘¦ plus three.
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So to make one final equation, we can replace star with š¯‘¦ and bow with š¯‘¦ plus three, resulting in the equation five š¯‘¦ plus seven times š¯‘¦ plus three equals 285.