Julia and Lena started reading a science fiction book at the same time. During the first week, Lena read $10$ more pages than Julia. The following week, Lena read $14$ pages, and Julia read the same number of pages she read the first week. Now they are on the same page. $\newline$ Which equation can you use to find $j$ , the number of pages Julia read during the first week? $\newline$ Choices: $\newline$ (A) $j + 10 + 14 = j + j$ $\newline$ (B) $j + 10 = j + j + 14$ $\newline$ How many pages did Julia read during the first week? $\newline$ $\_\_\_$ pages

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Grade 8

Solve equations with variables on both sides: word problems

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Q. Julia and Lena started reading a science fiction book at the same time. During the first week, Lena read

10

more pages than Julia. The following week, Lena read

14

pages, and Julia read the same number of pages she read the first week. Now they are on the same page.

\newline

Which equation can you use to find

j

, the number of pages Julia read during the first week?

\newline

Choices:

\newline

(A)

j + 10 + 14 = j + j

\newline

(B)

j + 10 = j + j + 14

\newline

How many pages did Julia read during the first week?

\newline

\_\_\_

pages

Understand the problem: Understand the problem. $\newline$ Julia and Lena start reading a book at the same time. Lena reads $10$ more pages than Julia in the first week. In the second week, Lena reads $14$ pages, and Julia reads the same number of pages as in the first week. They end up on the same page after the second week.
Set up the equation: Set up the equation based on the information given. $\newline$ Let $j$ represent the number of pages Julia read during the first week. Then Lena read $j + 10$ pages during the first week. In the second week, Julia read $j$ pages again, and Lena read $14$ pages. Since they are now on the same page, the total number of pages read by Julia and Lena must be equal.
Translate the situation: Translate the situation into an equation. $\newline$ The total number of pages Julia read in two weeks is $j$ (first week) + $j$ (second week). The total number of pages Lena read is $j + 10$ (first week) + $14$ (second week). Since they are on the same page, these two expressions must be equal.
Choose the correct equation: Choose the correct equation from the choices given. $\newline$ (A) $j + 10 + 14 = j + j$ $\newline$ (B) $j + 10 = j + j + 14$ $\newline$ The correct equation must equate the total pages read by Julia to the total pages read by Lena. Choice (A) adds Lena's reading from both weeks and equates it to Julia's total reading. Choice (B) only considers Lena's reading from the first week and equates it to Julia's total reading plus the $14$ pages Lena read in the second week. Therefore, the correct equation is (A).
Solve the equation: Solve the equation from choice (A) to find the number of pages Julia read during the first week. $\newline$ $j + 10 + 14 = j + j$ $\newline$ Combine like terms: $\newline$ $j + 24 = 2j$ $\newline$ Subtract $j$ from both sides: $\newline$ $24 = j$
Verify the solution: Verify the solution. $\newline$ If Julia read $24$ pages during the first week, then Lena read $24 + 10 = 34$ pages. In the second week, Julia again read $24$ pages, and Lena read $14$ pages. The total for Julia is $24 + 24 = 48$ pages, and for Lena, it is $34 + 14 = 48$ pages. Since both totals are equal, the solution is correct.