Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. Two students in Mr. Mitchell's class, Matt and Ruth, have been assigned a workbook to complete at their own pace. They get together at Matt's house after school to complete as many pages as they can. Matt has already completed 81 pages and will continue working at a rate of 1 page per hour. Ruth has completed 59 pages and can work at a rate of 12 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, Matt and Ruth 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. Mitchell's class, Matt and Ruth, have been assigned a workbook to complete at their own pace. They get together at Matt's house after school to complete as many pages as they can. Matt has already completed 81 pages and will continue working at a rate of 1 page per hour. Ruth has completed 59 pages and can work at a rate of 12 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, Matt and Ruth 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 it will take for Matt and Ruth to be on the same page. Let M represent the total number of pages Matt will have completed. Let R represent the total number of pages Ruth will have completed.  We can write two equations to represent the situation: For Matt: M = 81 + 1*x (since Matt has already completed 81 pages and works at a rate of 1 page per hour). For Ruth: R = 59 + 12*x (since Ruth has already completed 59 pages and works at a rate of 12 pages per hour).  Since they will eventually be working on the same page, we set M equal to R: 81 + 1*x = 59 + 12*xWrite Equations: Now we solve for x using substitution: 81 + x = 59 + 12x Subtract x from both sides: 81 = 59 + 11x Subtract 59 from both sides: 22 = 11x Divide both sides by 11: x = 2Solve for x: Now that we have the value of x, we can find out how many pages each student will have completed after 2 hours: For Matt: M = 81 + 1*2 = 81 + 2 = 83 pages For Ruth: R = 59 + 12*2 = 59 + 24 = 83 pages

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