Adam has 112 blue marbles.
He has 4 times as many blue marbles than red marbles.
After he gives away an equal number of blue and red marbles,
the number of blue marbles is 5 times that of the red marbles.
- How many blue marbles are there in the end?
- How many red marbles are there in the end?
- How many marbles are there in the end?
- How many marbles does Adam give away?
|
Blue marbles |
Red marbles |
Difference |
Before |
4 x 4 = 16 u |
1 x 4 = 4 u |
3 x 4 = 12 u |
Change |
- ? |
- ? |
|
After |
5 x 3 = 15 u |
1 x 3 = 3 u |
4 x 3 = 12 u |
(a)
The difference in the number between the blue and red marbles at first and in the end remains unchanged.
LCM of 3 and 4 is 12.
16 u = 112
1 u = 112 ÷ 16 = 7
Number of blue marbles in the end
= 15 u
= 15 x 7
= 105
(b)
Number of red marbles in the end
= 3 u
= 3 x 7
= 21
(c)
Total number of marbles in the end
= 105 + 21
= 126
(d)
Total number of marbles that Adam gives away
= (16 u - 15 u) x 2
= 1 u x 2
= 2 u
= 2 x 7
= 14
Answer(s): (a) 105; (b) 21; (c) 126; (d) 14