Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Two students in Mr. Hoover's class, Bonnie and Hunter, have been assigned a workbook to complete at their own pace. They get together at Bonnie's house after school to complete as many pages as they can. Bonnie has already completed 35 pages and will continue working at a rate of 7 pages per hour. Hunter has completed 37 pages and can work at a rate of 6 pages per hour. Eventually, the two students will be working on the same page. How long will that take? How many pages will each of them have completed? After _____ hours, Bonnie and Hunter will have each completed _____ pages in their workbooks.

Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.  Two students in Mr. Hoover's class, Bonnie and Hunter, have been assigned a workbook to complete at their own pace. They get together at Bonnie's house after school to complete as many pages as they can. Bonnie has already completed 35 pages and will continue working at a rate of 7 pages per hour. Hunter has completed 37 pages and can work at a rate of 6 pages per hour. Eventually, the two students will be working on the same page. How long will that take? How many pages will each of them have completed?   After _____ hours, Bonnie and Hunter will have each completed _____ pages in their workbooks.

Bytelearn · Accepted Answer

Define Variables: Let's define the variables: Let x represent the number of hours after they start working at Bonnie's house. Let B represent the total number of pages Bonnie has completed. Let H represent the total number of pages Hunter has completed.Write Equations: We can write two equations to represent the situation: For Bonnie: B = 35 + 7x (since she has already completed 35 pages and works at a rate of 7 pages per hour) For Hunter: H = 37 + 6x (since he has already completed 37 pages and works at a rate of 6 pages per hour)Set Equations Equal: We want to find out when Bonnie and Hunter will have completed the same number of pages, so we set the two equations equal to each other: 35 + 7x = 37 + 6xSolve for x: Now, we solve for x by subtracting 6x from both sides of the equation: 35 + 7x - 6x = 37 + 6x - 6x 35 + x = 37Subtract to Solve: Next, we subtract 35 from both sides to solve for x: 35 + x - 35 = 37 - 35 x = 2Find Pages Completed: Now that we have the value of x, we can find out how many pages each student has completed after 2 hours: For Bonnie: B = 35 + 7(2) = 35 + 14 = 49 pages For Hunter: H = 37 + 6(2) = 37 + 12 = 49 pages

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