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system of equations by graphing: word problemsHome / SchoologyGmailMSCIDONTHAYou have piasLearn with an example Watch a videoTwo classmates have decided to read all the volumes in a popular series of books. Sarah has already read volumes and will continue to read new ones at a rate of volume per week. Eva, who hasn't started reading the series yet, will read volumes per week. At some point, Eva will catch up with Sarah and they will be reading the same book. How long will that take?Write a system of equations, graph them, and type the solution.SarahEva
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Q. system of equations by graphing: word problemsHome / SchoologyGmailMSCIDONTHAYou have piasLearn with an example Watch a videoTwo classmates have decided to read all the volumes in a popular series of books. Sarah has already read volumes and will continue to read new ones at a rate of volume per week. Eva, who hasn't started reading the series yet, will read volumes per week. At some point, Eva will catch up with Sarah and they will be reading the same book. How long will that take?Write a system of equations, graph them, and type the solution.SarahEva
- Define variables: Let's define variables: Let be the number of weeks Sarah reads, and be the number of weeks Eva reads.
- Write Sarah's equation: Write Sarah's equation: Sarah has read volumes and reads more each week, so her total volumes read is .
- Write Eva's equation: Write Eva's equation: Eva starts at volumes and reads volumes each week, so her total volumes read is .
- Set up system of equations: Set up the system of equations where the number of volumes read by Sarah equals the number of volumes read by Eva: .
- Equal number of weeks: Since Eva will catch up with Sarah, they will have read for the same number of weeks: .
- Substitute and simplify: Substitute for in the equation: .
- Solve for s: Solve for : .
- Divide and calculate: Simplify the equation: .
- Divide and calculate: Simplify the equation: . Divide both sides by to find : .
- Divide and calculate: Simplify the equation: . Divide both sides by to find : . Calculate the value of : .
