A bag contains marbles of three different colours red, blue , yellow. 2/5 of the marbles are red. The ratio of the number of blue marbles to the number of yellow marbles is 5:7. What fraction of the marbles in the bag is blue? There are 54 more red marbles than blue marbles. How many marbles are there in the bag?

Question

Reiny · Accepted Answer

let the total be x
(2/5)x = r , also b+54 = (2/5)x
b = 2x/5 - 54 = (2x - 270)/5

b : y = 5 : 7
5y = 7b
y = (7/5)b
y = 7(2x-270)/25

so 2x/5 + (2x-270)/5 + 7(2x-270)/25 = x
times 25
10x + 10x - 1350 + 14x - 1890 = 25x
-9x = -3240
x = 360

we have 510 marbles

check:
red = (2/5)(360) = 144
b = (720-270)/5 = 90
y = (7/5)(90) = 126

144+90+126 = 360 , check!
blue : yellow = 90 : 126 = 5 : 7 , check
area there 54 more reds than blues?
144-90 = 54, check!

there are 510 marbles

Reiny · Answer

I obviously got x = 360 So there are 360 marbles, I have no idea where I got the 510 from, and then I copied it again at the end. Time for my third cup of coffee.