Sarabeth is selling bracelets as a fundraiser for the school library. Each bracelet with blue beads sells for $4.50. Each bracelet with red beads sells for $5. She raised a total of $130 for the library.The number of bracelets with red beads (r) that Sarabeth sold is 3 less than twice the number of bracelets with blue beads (b) sold. If the table is used to guess and check, what equation should go in the top of the third column?

Without the exact given table, here is the most detail I can provide:
blue bracelets: b
red bracelets: r = 2b - 3
revenue = 4.5b + 5r = 4.5b + 5(2b - 3) = 14.5b - 15 (The "equation for the third column" is likely to be from this.)
Given that revenue = 130, we must find an integer value for b that results in revenue = 130:
14.5b - 15 = 130
14.5b = 145
b = 10
Therefore there were 10 blue bracelets and (2*10 - 3) = 17 red bracelets sold.