Adam has 42 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 2 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 1 = 6 u |
1 x 1 = 1 u |
5 x 1 = 5 u |
Change |
+ ? |
+ ? |
|
After |
2 x 5 = 10 u |
1 x 5 = 5 u |
1 x 5 = 5 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 1 is 5.
6 u = 42
1 u = 42 ÷ 6 = 7
Number of blue beads in the end
= 10 u
= 10 x 7
= 70
(b)
Number of red beads in the end
= 5 u
= 5 x 7
= 35
(c)
Total number of beads in the end
= 70 + 35
= 105
(d)
Total number of beads that Adam buys
= (10 u - 6 u) x 2
= 4 u x 2
= 8 u
= 8 x 7
= 56
Answer(s): (a) 70; (b) 35; (c) 105; (d) 56