Adam has some blue stickers and green stickers.
If 45 blue stickers are added, 70% of the stickers will be green stickers.
If 210 blue stickers are added, 40% of the stickers will be green stickers.
- How many blue stickers are there?
- How many green stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Blue |
Green |
Blue |
Green |
Before |
6 u - 45 |
14 u |
21 u - 210 |
14 u |
Change |
+ 45 |
No change |
+ 210 |
No change |
After |
3x2 = 6 u |
7x2 = 14 u |
3x7 = 21 u |
2x7 = 14 u |
(a)
70% =
70100 =
71040% =
40100 =
25 Scenario 1 Fraction of the stickers that are blue in the end
= 1 -
710 =
310 Scenario 2
Fraction of the stickers that are blue in the end
= 1 -
25 =
35 The number of green stickers remains unchanged in both scenarios.
LCM of 7 and 2 = 14
21 u - 210 = 6 u - 45
21 u - 6 u = 210 - 45
15 u = 165
1 u = 165 ÷ 15 = 11
Number of blue stickers
= 6 u - 45
= 6 x 11 - 45
= 66 - 45
= 21
(b)
Number of green stickers
= 14 u
= 14 x 11
= 154
Answer(s): (a) 21; (b) 154