1. **Problem Statement:** A total sum of 700 is to be distributed as seven cash prizes such that each prize is 20 less than the previous one. We need to find the value of each prize. 2. **Define variables:** Let the first prize be $x$. Then the prizes are: $$x, x-20, x-40, x-60, x-80, x-100, x-120$$ 3. **Sum of prizes:** The sum of all seven prizes is given as 700. So, $$x + (x-20) + (x-40) + (x-60) + (x-80) + (x-100) + (x-120) = 700$$ 4. **Simplify the equation:** $$7x - (20 + 40 + 60 + 80 + 100 + 120) = 700$$ Calculate the sum inside the parentheses: $$20 + 40 + 60 + 80 + 100 + 120 = 420$$ So, $$7x - 420 = 700$$ 5. **Solve for $x$:** $$7x = 700 + 420 = 1120$$ $$x = \frac{1120}{7} = 160$$ 6. **Find all prizes:** $$160, 140, 120, 100, 80, 60, 40$$ 7. **Answer:** The prizes are 160, 140, 120, 100, 80, 60, and 40 respectively.