Adam has 180 blue beads.
He has 6 times as many blue beads as red beads.
After he buys an equal number of blue and red beads,
the number of blue beads is 3 times that of the red beads.
- How many blue beads are there in the end?
- How many red beads are there in the end?
- How many beads are there in the end?
- How many beads does Adam buy?
|
Blue beads |
Red beads |
Difference |
Before |
6 x 2 = 12 u |
1 x 2 = 2 u |
5 x 2 = 10 u |
Change |
+ ? |
+ ? |
|
After |
3 x 5 = 15 u |
1 x 5 = 5 u |
2 x 5 = 10 u |
(a)
The difference in the number between the blue and red beads at first and in the end remains unchanged.
LCM of 5 and 2 is 10.
12 u = 180
1 u = 180 ÷ 12 = 15
Number of blue beads in the end
= 15 u
= 15 x 15
= 225
(b)
Number of red beads in the end
= 5 u
= 5 x 15
= 75
(c)
Total number of beads in the end
= 225 + 75
= 300
(d)
Total number of beads that Adam buys
= (15 u - 12 u) x 2
= 3 u x 2
= 6 u
= 6 x 15
= 90
Answer(s): (a) 225; (b) 75; (c) 300; (d) 90