This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

## Tuesday, July 20, 2010

### ACS Primary 2009 PSLE Math Prelim Paper 2 Q18

There were some black and white marbles in a bag. If 20 black marbles are removed from the bag, the total number of marbles will be 7 times the number of black marbles left. If 50 white marbles are removed from the bag, the total number of marbles left will be 5 times the number of black marbles left. How many marbles are there in the bag?

Solution

20 black marbles (removed)
Black --> 1 unit + (20)
White --> 6 units

50 white marbles (removed)
Black --> 1 part
White --> 4 parts + (50)

(Black) 1 unit + 20 --> 1 part ...... (x4)*
(White) 6 units --> 4 parts + 50

(Black) 4 units + 80 --> 4 parts
(White) 6 units --> 4 parts + 50

*(x4) to make an equal number of 4 parts for both Black and White Marbles

(White Marbles) - (Black Marbles)
6 units - 4 units - 80 --> 4 parts + 50 - 4 parts
2 units - 80 --> 50
2 units --> 50 + 80
2 units --> 130
1 unit --> 130 divided by 2 = 65

Total number of marbles
Black --> 1 unit + 20
White --> 6 units
--> 7 units + 20
= (7 x 65) + 20
= 475

Answer: 475 marbles

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