There are two sizes of red and blue marbles in a box. if the big marbles in the box, 45 are red and 3/4 are blue. the fraction of small marbles that are red is 2/5 and the fraction of small marbles that are are blue is 3/5. there are 24 more small blue marbles than small red marbles. what percent of the marbles are big marbles?

Let
x------> amount of  big marbles in the box
y------> amount of  small marbles in the box
R----> amount of  small marbles that are red in the box
B----> amount of  small marbles that are blue in the box

we know that
x=45+(3/4)*x----> x-(3/4)*x=45----> x/4=45-----> x=180

R+B=y-----> equation 1
R=(2/5)*y---> equation 2
B=(3/5)*y---> equation 3
B=R+24----> equation 4

substitute equation 2 in equation 1
[(2/5)*y]+B=y----> equation 5

substitute equation 2 in equation 4
B=[(2/5)*y]+24----> equation 6

resolve the system
[(2/5)*y]+B=y---> multiply by 5----> 2y+5B=5y----> 3y=5B
B=[(2/5)*y]+24----> multiply by 5----> 5B=2y+120

using a graph tool
see the attached figure

the solution is
B=72
y=120
R=y-B----> R=48

total marbies=x+y-----> 180+120-----> 300
tota; big marbies=180
percent of the marbles are big marbles
if 100%-----------> 300
 X----------------> 180
x=180*100/300-----> x=60%

the answer is
60%