Adam has some green stickers and blue stickers.
If 31 green stickers are added, 70% of the stickers will be blue stickers.
If 311 green stickers are added, 30% of the stickers will be blue stickers.
- How many green stickers are there?
- How many blue stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Green |
Blue |
Green |
Blue |
Before |
9 u - 31 |
21 u |
49 u - 311 |
21 u |
Change |
+ 31 |
No change |
+ 311 |
No change |
After |
3x3 = 9 u |
7x3 = 21 u |
7x7 = 49 u |
3x7 = 21 u |
(a)
70% =
70100 =
71030% =
30100 =
310 Scenario 1 Fraction of the stickers that are green in the end
= 1 -
710 =
310 Scenario 2
Fraction of the stickers that are green in the end
= 1 -
310 =
710 The number of blue stickers remains unchanged in both scenarios.
LCM of 7 and 3 = 21
49 u - 311 = 9 u - 31
49 u - 9 u = 311 - 31
40 u = 280
1 u = 280 ÷ 40 = 7
Number of green stickers
= 9 u - 31
= 9 x 7 - 31
= 63 - 31
= 32
(b)
Number of blue stickers
= 21 u
= 21 x 7
= 147
Answer(s): (a) 32; (b) 147