Please post the original question from next time. It is very difficult to get any idea from the solution approach only. Anyways, here is the original question for the help of others,

A company sells only pens and pencils. The revenue from pen sales in 2007 was up 5% from 2006, but the revenue from pencil sales declined 13% over the same period. If overall revenue was down 1% from 2006 to 2007, what was the ratio of pencil revenue to pen revenue in 2006?

From the screenshot you posted, it is evident that the book assumed in 2006, the revenue from pen sales was $100 and revenue from pencil sales was $x.

Hence, the total revenue in 2006 = $(100 + x)

Now, in 2007, the revenue from pen sales = $(100 + 5% of 100) = $105
And revenue from pencil sales = $(x - 13% of x) = $0.87x
Hence, the total revenue in 2007 = $(105 + 0.87x) [This is one way to get overall revenue of 2007]

But, the question said that "overall revenue was down 1% from 2006 to 2007".
Hence, total revenue in 2007 = (0.99)*(Total revenue in 2006) = $(0.99)*(100 + x) [This is another way to get overall revenue of 2007]

Hence, (0.99)*(100 + x) = (105 + 0.87x)
-----> 99 + 0.99x = 105 + 0.87x
-----> (0.99 - 0.87)x = (105 - 99)
-----> 0.12x = 6
-----> x = 50

Hence, ratio of pencil revenue to pen revenue in 2006 = x/100 = 50/100 = 1/2