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Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Two classmates have decided to read all the volumes in a popular series of books. Annie has already read volumes and will continue to read new ones at a rate of volume per week. Amy, who hasn't started reading the series yet, will read volumes per week. At some point, Amy will catch up with Annie and they will be reading the same book. How long will that take? How many volumes will each girl have read by then?In weeks, the girls will each have read volumes in the series.
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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Two classmates have decided to read all the volumes in a popular series of books. Annie has already read volumes and will continue to read new ones at a rate of volume per week. Amy, who hasn't started reading the series yet, will read volumes per week. At some point, Amy will catch up with Annie and they will be reading the same book. How long will that take? How many volumes will each girl have read by then?In weeks, the girls will each have read volumes in the series.
- Define Variables: Let's define the variables.Let represent the number of weeks it will take for Amy to catch up with Annie.Annie has already read volumes and reads volume per week, so the total number of volumes Annie will have read after weeks is .Amy hasn't started reading yet and will read volumes per week, so the total number of volumes Amy will have read after weeks is .
- Set Equations: Set up the equations based on the information given.Annie's volumes: Amy's volumes: Since Amy will catch up with Annie, the number of volumes read by both will be the same at some point, so we can set the equations equal to each other:
- Solve Equation: Solve the equation for . Subtract from both sides to get:
- Calculate Volumes: Determine the number of volumes each girl will have read by the time Amy catches up with Annie.Since represents the number of weeks, it will take weeks for Amy to catch up with Annie.Now we need to calculate the number of volumes each girl will have read by then.Annie's volumes after weeks: Amy's volumes after weeks:
