Simon keeps some black and white marbles in Box A. He also keeps some green and
blue marbles in Box B. There were 1 3/5 times as many black as white marbles. The ratio
of the number of white marbles to the total number of green and blue marbles is 8:
5. When Simon buys 138 more green and blue marbles, the ratio of the number of
black marbles to the total number of green and blue marbles becomes 4:3.
a) Find the ratio of the number of black marbles to the number of blue and green
marbles in the boxes at first?
b) How many more black marbles than white marbles are there in Box A?
B==Black, W==White, G==Green, L==Blue
[G + L]==M
B ==8/5W
W /[M]==8/5
B/[M + 138] ==4 / 3, solve for B, W, M
B==384, W==240, M==150
a) B : M ==384 : 150 == 64 : 25
b) 384 - 240 == 144
+313 This question is really hard. A math question with mixed numbers with this is really hard so it is easy to convert them to improper fractions.
Box A Box B
W = x G
B = 8/5x BL
White marbles = x
Black marbles B = 8/5x
\({X \over G + BL } = {8 \over 5} —- (1)\)
\({B\over G + BL + 138} = {4\over 3} —- (2)\)
Find B/G+BL = ?
B/G+BL = 8/5x/(G+BL) = 8/5(X/G+BL)
= 8/5 * 8/5 (From (1)).
= 64/25
So Ratio of Black marbles to the number of Blue and Green marbles = 64:25
X/G+BL = 8/5 ----(1)
So G+BL = 5x/8 --> Substitute in (2)
B/G+BL+138 = 4/3
B/5x/8 + 138 = 4/3
ie. 8/5x/8 + 138 = 4/3
24/5x = 20x/8 + 552
\( {192 - 100 \over 40}x = 552\)
So x = 552 * 40/92 + 240
when x = 240
B = 8/5x = 8/5 * 240
= 384
G + BL = 5x/8 = 150
Ans: Box A has 240 white marbles and 384 blue marbles So 384 - 240 = 144 more black marbles than white marbles.
