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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two classmates got together over the weekend to do their assigned History reading. Kathleen can read pages per minute, while Tanvi can read pages per minute. When they met, Kathleen had already read pages, and Tanvi had already gotten through pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take?Kathleen and Tanvi had each read pages after minutes.
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Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two classmates got together over the weekend to do their assigned History reading. Kathleen can read pages per minute, while Tanvi can read pages per minute. When they met, Kathleen had already read pages, and Tanvi had already gotten through pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take?Kathleen and Tanvi had each read pages after minutes.
- Define Variables: Let's define the variables.Let be the number of minutes they read together.Let be the total number of pages each had read after minutes.Kathleen's reading speed is pages per minute, and she had already read pages.Tanvi's reading speed is pages per minute, and she had already read pages.
- Write Equations: Write the equations based on the given information.For Kathleen: For Tanvi:
- Substitution to Solve: Use substitution to solve for . Since both equations equal , we can set them equal to each other:
- Solve for x: Solve the equation for x.
- Find Total Pages: Use the value of to find , the total number of pages read.We can use either equation, but let's use Kathleen's equation:$y = \(119\)
