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Question

Hi again.. another question needs help. Thank you.

Bag Z had 32 marbles more than Bag Y and Bag Y had 14 marbles more than Bag X. The total number of marbles in Bags Y and Z was 8 times the number of marbles in Bag X.

a) How many marbles should be moved from Bag Z to Bag Y so that these two bags would contain the same amount of marbles?

b) What was the total number of marbles in Bags X, Y and Z?

Answer

(a)
32/2 = 16

(b)
marbles in Bag —
X : 1 unit
Y : 1 unit + 14
Z : 1 unit + 14 + 32 = 1 unit + 46

1 unit + 14 + 1 unit + 46 = 2 units + 60
2 units + 60 = 1 unit x 8 = 8 units
1 unit = 60/(8 – 2) = 10
1 unit + 1 unit + 14 + 1 unit + 46 = 3 units + 60 = 3 x 10 + 60 = 90

Ans : (a) 16 marbles; (b) 90 marbles.

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This is a Part Whole question. 

Bag Y is the common  item. 

   Y   X    Z + Y
R 1u 1u – 14 1u + 32 2u + 32
  24 10 56 90

(2u + 32) / 8 = (1u – 14) /1 

2u + 32 = 8u – 112

32 + 112 = 8u – 2u

6u = 144

1u = 144 ÷ 6 = 24

a)

(56 + 24) / 2 = 40

56 – 40 = 16

b)

24 + 10 + 56 = 90

 

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