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. Which equation can you use to find j, the number of pages Julia read during the first week? Choices: (A)j + 10 + 14 = j + j (B)j + 10 = j + j + 14 How many pages did Julia read during the first week? ____ pages

Question

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. Which equation can you use to find j, the number of pages Julia read during the first week?   Choices: (A)j + 10 + 14 = j + j (B)j + 10 = j + j + 14  How many pages did Julia read during the first week?   ____ pages

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. 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. 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. 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. (A) j + 10 + 14 = j + j (B) j + 10 = j + j + 14 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. j + 10 + 14 = j + j Combine like terms: j + 24 = 2j Subtract j from both sides: 24 = jVerify the solution: Verify the solution. 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.

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