Adam has 162 blue marbles.
He has 6 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 4 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 |
6 x 3 = 18 u |
1 x 3 = 3 u |
5 x 3 = 15 u |
Change |
+ ? |
+ ? |
|
After |
4 x 5 = 20 u |
1 x 5 = 5 u |
3 x 5 = 15 u |
(a)
The difference in the number between the blue and red marbles at first and in the end remains unchanged.
LCM of 5 and 3 is 15.
18 u = 162
1 u = 162 ÷ 18 = 9
Number of blue marbles in the end
= 20 u
= 20 x 9
= 180
(b)
Number of red marbles in the end
= 5 u
= 5 x 9
= 45
(c)
Total number of marbles in the end
= 180 + 45
= 225
(d)
Total number of marbles that Adam buys
= (20 u - 18 u) x 2
= 2 u x 2
= 4 u
= 4 x 9
= 36
Answer(s): (a) 180; (b) 45; (c) 225; (d) 36