Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ 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? $\newline$ After $\_$ hours, Bonnie and Hunter will have each completed $\_$ pages in their workbooks.

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Solve a system of equations using substitution: word problems

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

\newline

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?

\newline

After

\_

hours, Bonnie and Hunter will have each completed

\_

pages in their workbooks.

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