TITLE: Cutting cake into 5 equal pieces
QUESTION [7 upvotes]: If a cake is cut into $5$ equal pieces, each piece would be $80$ grams
  heavier than when the cake is cut into $7$ equal pieces. How heavy is
  the cake?

How would I solve this problem? Do I have to try to find an algebraic expression for this? $5x = 7y + 400$?

REPLY [3 votes]: $$\frac{w}{5}=\frac{w}{7}+80$$
Multiply both sides by 35
$$7w=5w+80\cdot 35$$
substracting both sides by $$2w$$
$$2w=80\cdot 35$$
dividing both sides by 2
$$w=40\cdot 35$$
So weight of cake is 1400