Adam has 51 blue marbles.
He has 3 times as many blue marbles as red marbles.
After he buys an equal number of blue and red marbles,
the number of blue marbles is 2 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 buy?
|
Blue marbles |
Red marbles |
Difference |
Before |
3 x 1 = 3 u |
1 x 1 = 1 u |
2 x 1 = 2 u |
Change |
+ ? |
+ ? |
|
After |
2 x 2 = 4 u |
1 x 2 = 2 u |
1 x 2 = 2 u |
(a)
The difference in the number between the blue and red marbles at first and in the end remains unchanged.
LCM of 2 and 1 is 2.
3 u = 51
1 u = 51 ÷ 3 = 17
Number of blue marbles in the end
= 4 u
= 4 x 17
= 68
(b)
Number of red marbles in the end
= 2 u
= 2 x 17
= 34
(c)
Total number of marbles in the end
= 68 + 34
= 102
(d)
Total number of marbles that Adam buys
= (4 u - 3 u) x 2
= 1 u x 2
= 2 u
= 2 x 17
= 34
Answer(s): (a) 68; (b) 34; (c) 102; (d) 34