1994 AHSME Problems/Problem 16
Some marbles in a bag are red and the rest are blue. If one red marble is removed, then one-seventh of the remaining marbles are red. If two blue marbles are removed instead of one red, then one-fifth of the remaining marbles are red. How many marbles were in the bag originally?
Let and be the number of red and blue marbles originally in the bag respectively. After red marble is removed, there are marbles left in the bag and red marbles left. So When blue marbles are removed, there are red marbles and total marbles left in the bag. So Cross multiplying for each yields We can equate each of these expressions to yields Therefore, the total number of marbles is
--Solution by TheMaskedMagician