Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks. $\newline$ Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bert can read $1$ page per minute, and he had already read $79$ pages. Preston, who has a reading speed of $3$ pages per minute, had read $9$ pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read? $\newline$ After $\_$ minutes, Bert and Preston had each read $\_$ pages.

Full solution

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

\newline

Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bert can read

1

page per minute, and he had already read

79

pages. Preston, who has a reading speed of

3

pages per minute, had read

9

pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?

\newline

After

\_

minutes, Bert and Preston had each read

\_

pages.

Define Variables: Let's define the variables: $\newline$ Let $x$ represent the number of minutes after they start reading together. $\newline$ Let $B$ represent the total number of pages Bert has read. $\newline$ Let $P$ represent the total number of pages Preston has read.
Write Equations: We can write two equations to represent the situation: $\newline$ For Bert: $B = 79 + 1 \times x$ (since Bert reads $1$ page per minute and had already read $79$ pages) $\newline$ For Preston: $P = 9 + 3 \times x$ (since Preston reads $3$ pages per minute and had already read $9$ pages)
Set Equations Equal: Since they eventually read the same number of pages, we can set the two equations equal to each other: $\newline$ $79 + x = 9 + 3x$
Solve for x: Now, we solve for $x$ using substitution: $\newline$ $79 + x = 9 + 3x$ $\newline$ Subtract $x$ from both sides: $\newline$ $79 = 9 + 2x$
Isolate x Term: Subtract $9$ from both sides to isolate the term with $x$ : $\newline$ $79 - 9 = 2x$ $\newline$ $70 = 2x$
Find x Value: Divide both sides by $2$ to solve for x: $\newline$ $\frac{70}{2} = x$ $\newline$ $35 = x$
Find Pages Read: Now that we have the value for $x$ , we can find out how many pages each of them read: $\newline$ For Bert: $B = 79 + 1 \times 35 = 79 + 35 = 114$ pages $\newline$ For Preston: $P = 9 + 3 \times 35 = 9 + 105 = 114$ pages