what percentage of the marbles are big marbles

Question

there are some red and blue marbles in a box. 45 big marbles are red and 3/4 of the marbles are blue . the ratio of the number of small red marbles to the number of small blue marbles is 2:3 . if there are 24 more small blue marbles than red marbles ,what percentage of the marbles are big marbles:)

Answer 1

Represent each marble by a 2-letter symbol: S=small, B=big, R=red, B=blue. First letter is the size.

Let N=total number of marbles=SR+SB+BR+BB=N.

BR=45,

SB+BB=3N/4,

SR/SB=2/3, SR=2SB/3,

SB=24+SR+BR=69+SR=69+2SB/3,

SB/3=69, SB=207, SR=2SB/3=138.

138+207+45+BB=N, N=BB+390.

207+BB=3N/4, 828+4BB=3N, N=(828+4BB)/3=BB+390,

828+4BB=3BB+1170, BB=1170-828=342,

N=BB+390=342+390=732.

Need to find 100(BR+BB)/N=100(45+342)/732=38700/732=52.87% approx.