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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?

 Oct 18, 2021
 #1
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+1

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

 Oct 23, 2021
 #2
avatar+286 
+1

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.

 Oct 24, 2021

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