Question

In a bag are blue green and red marbles. 50% are blue and thirty percent are green. There are 6 red marbles in the bag. If you increase the number of blue marbles by 40%, how many blue marbles will be in the bag

Answer 1

There will be 21 blue marbles

Explanation:

In a bag are blue, green and red marbles. Let x be the number of all marbles in the bag.

50% of all marbles are blue. 50% is exactly half of the marbles, so there are
`(x)/(2)` blue marbles.

30% of all marbles are green, so there are
`x\cdot 0.3=0.3x` green marbles.

The rest marbles are red marbles, so there are
`x-(1)/(2)x-0.3x=x-0.5x-0.3x=0.2x` red marbles.

There are 6 red marbles in the bag, thus

`0.2x=6\\ \\2x=60\\ \\x=30`

Hence, there are

• 
  `30\cdot (1)/(2)=15` blue marbles;
• 
  `30\cdot 0.3=9` green marbles;
• 6 red marbles.

If you increase the number of blue marbles by 40%, then

15 - 100%

x - 140% (increased by 40%)

Write a proportion:

`(15)/(x)=(100)/(40)`

Cross multiply:

`100x=15\cdot 140\\ \\100x=2,100\\ \\x=21`