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## Friday, February 19, 2010

### Nanyang Pri Sch 2009 P6 CA1 Math Paper 2 Q17

John had some red and blue marbles in a box. The sum of 1/4 of the red marbles and 2/5 of the blue marbles in the box is 64. The sum of 3/4 of the red marbles and 4/5 of the blue marble in the box is 144.
a) How many red marbles are there in the box?
b) How many blue marbles are there in the box?

Solution

Red (all marbles) --> R R R R
Blue (all marbles) --> B B B B B

1/4 or red marbles and 2/5 or blue marbles -- > 64
R + B B --> 64

3/4 of red marble and 4/5 of blue marbles --> 144
R R R + B B B B --> 144

R + B B --> 64 (multiply all by 2)
R R + B B B B --> 128

We now have
R R R + B B B B --> 144
R R + B B B B --> 128

R --> 144 - 128 = 16

a)
Number of Red Marbles
R R R R --> 4 x 16 = 64

Answer: 64 red marbles

b)
R + B B --> 64
16 + B B --> 64
B B --> 64 - 16 = 48
B --> 48 divided by 2 = 24

Number of Blue Marbles
B B B B B --> 5 x 24 = 120

Answer: 120 blue marbles