MATH SOLVE

6 months ago

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.