Q:

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

A:
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.