Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. $\newline$ Two classmates got together over the weekend to do their assigned History reading. Sandra can read $3$ pages per minute, while Ronald can read $2$ pages per minute. When they met, Sandra had already read $21$ pages, and Ronald had already gotten through $50$ 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? $\newline$ After $\_\_\_$ minutes, Sandra and Ronald had each read $\_\_\_$ pages.

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Solve a system of equations using any method: word problems

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Q. Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.

\newline

Two classmates got together over the weekend to do their assigned History reading. Sandra can read

3

pages per minute, while Ronald can read

2

pages per minute. When they met, Sandra had already read

21

pages, and Ronald had already gotten through

50

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?

\newline

After

\_\_\_

minutes, Sandra and Ronald had each read

\_\_\_

pages.

Define Reading Rates: Let's denote the time they both read together as $t$ (in minutes). Sandra's reading rate is $3$ pages per minute, and Ronald's is $2$ pages per minute. Sandra had a head start of $21$ pages, and Ronald had a head start of $50$ pages.
Write Equations: We can write the equation for the total number of pages Sandra has read as: Total pages Sandra read = $3t + 21$ .
Set Equations Equal: Similarly, the equation for the total number of pages Ronald has read is: Total pages Ronald read = $2t + 50$ .
Solve for Time: Since they have read the same number of pages after $t$ minutes, we can set the two equations equal to each other: $3t + 21 = 2t + 50$ .
Calculate Pages Read: Now, we solve for $t$ by subtracting $2t$ from both sides: $3t - 2t + 21 = 2t - 2t + 50$ , which simplifies to $t + 21 = 50$ .
Final Result: Subtracting $21$ from both sides gives us $t = 50 - 21$ , which means $t = 29$ .
Final Result: Subtracting $21$ from both sides gives us $t = 50 - 21$ , which means $t = 29$ .Now that we have the time, we can calculate the total number of pages each has read. For Sandra: $3 \times 29 + 21 = 87 + 21 = 108$ pages.
Final Result: Subtracting $21$ from both sides gives us $t = 50 - 21$ , which means $t = 29$ . Now that we have the time, we can calculate the total number of pages each has read. For Sandra: $3 \times 29 + 21 = 87 + 21 = 108$ pages. For Ronald: $2 \times 29 + 50 = 58 + 50 = 108$ pages.
Final Result: Subtracting $21$ from both sides gives us $t = 50 - 21$ , which means $t = 29$ . Now that we have the time, we can calculate the total number of pages each has read. For Sandra: $3 \times 29 + 21 = 87 + 21 = 108$ pages. For Ronald: $2 \times 29 + 50 = 58 + 50 = 108$ pages. Therefore, after $29$ minutes, Sandra and Ronald had each read $108$ pages.