The applicable relationships are
... markup = (markup %)/100% × cost
... cost + markup = price
The purpose of dividing by 100% is to change the markup percentage to a decimal number. Effectively, you're removing the percent sign and shifting the decimal point 2 places to the left.
In each case, fill in the numbers you know and solve for the values you don't know.
1. markup = 65.3%/100%×$120.37 = 0.653×$120.37 = $78.60
... price = $120.37 + 78.60 = $198.97
2. markup = 100%/100%×$0.43 = 1.00×$0.43 = $0.43
... price = $0.43 + 0.43 = $0.86
3. markup = (markup %)/100% × cost
You will note that (markup %) has a multiplier. Multiply the equation by the reciprocal of that. This gives you the formula for (markup %).
... markup/cost × 100% = (markup %)
... $572.59/$427.41 × 100% = (markup %)
... 1.339674 × 100% = (markup %)
... 134.0% = markup % . . . . . . . . . rounded to the nearest tenth %
... price = $427.41 + 572.59 = $1000.00
4. Same as 3.
... markup % = $10.13/$67.50 × 100% = 15.0%
... price = $67.50 + 10.13 = $77.63
5. cost + markup = price
... $19.00 + markup = $26.60
... markup = $7.60 . . . . . . . . . . . . . . . subtract $19.00
... markup % = $7.60 /$19.00 × 100% = 40.0%
