Catalina must deliver a report for her work and has three days to complete it. On the first day Catalina completed 2/7 of the report, on the second day 3/5 of the rest and completed the last 10 pages of her report on the third day. How many pages did Catherine write in her report?

Accepted Solution

Let's break down Catalina's progress step by step. $$\text{On the first day, Catalina completed }\(2/7\)\text{ of the report. Let T be the total number of pages in the report. On the first day, she completed }\((2/7)T\)\text{ pages, leaving }\((5/7)T\) \text{pages.}$$ $$\text{On the second day, she completed }\(3/5\)\text{ of the remaining report, which is }\((3/5) \cdot (5/7)T\) \text{pages. This means she has }\((2/5) \cdot (5/7)T\)\text{ pages left.}$$ On the third day, she completed the remaining 10 pages. Now, we can set up an equation to solve for T, the total number of pages in the report: $$\((2/7)T + (3/5) \cdot (5/7)T + 10 = T\)$$ First, simplify the fractions: $$\((2/7)T + (3/7)T + 10 = T\)$$ Now, combine like terms: $$\((5/7)T + 10 = T\)$$ $$\text{Subtract }\(5/7\)\text{T from both sides:}$$ $$\(10 = (2/7)T\)$$ $$\text{Now, isolate T by multiplying both sides by }\(7/2\)\text{ (or dividing by }\(2/7\)):$$ $$\(T = 10 \cdot (7/2) = 35\)$$ So, Catalina wrote a total of 35 pages in her report.