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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 got together over the weekend to do their assigned History reading. Sandra can read pages per minute, while Ronald can read pages per minute. When they met, Sandra had already read pages, and Ronald had already gotten through pages. After a while, they had both read the same number of pages. How long did that take? How many pages had each one read?After minutes, Sandra and Ronald had each read pages.
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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 got together over the weekend to do their assigned History reading. Sandra can read pages per minute, while Ronald can read pages per minute. When they met, Sandra had already read pages, and Ronald had already gotten through pages. After a while, they had both read the same number of pages. How long did that take? How many pages had each one read?After minutes, Sandra and Ronald had each read pages.
- Define Reading Rates: Let's denote the time they both read together as (in minutes). Sandra's reading rate is pages per minute, and Ronald's is pages per minute. Sandra had a head start of pages, and Ronald had a head start of pages.
- Write Equations: We can write the equation for the total number of pages Sandra has read as: Total pages Sandra read = .
- Set Equations Equal: Similarly, the equation for the total number of pages Ronald has read is: Total pages Ronald read = .
- Solve for Time: Since they have read the same number of pages after minutes, we can set the two equations equal to each other: .
- Calculate Pages Read: Now, we solve for by subtracting from both sides: , which simplifies to .
- Final Result: Subtracting from both sides gives us , which means .
- Final Result: Subtracting from both sides gives us , which means .Now that we have the time, we can calculate the total number of pages each has read. For Sandra: pages.
- Final Result: Subtracting from both sides gives us , which means . Now that we have the time, we can calculate the total number of pages each has read. For Sandra: pages. For Ronald: pages.
- Final Result: Subtracting from both sides gives us , which means . Now that we have the time, we can calculate the total number of pages each has read. For Sandra: pages. For Ronald: pages. Therefore, after minutes, Sandra and Ronald had each read pages.
