Adam has some green stickers and blue stickers.
If 102 green stickers are added, 30% of the stickers will be blue stickers.
If 162 blue stickers are added, 10% of the stickers will be green stickers.
- How many green stickers are there?
- How many blue stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Green |
Blue |
Green |
Blue |
Before |
7 u - 102 |
3 u |
1 p |
9 p - 162 |
Change |
+ 102 |
No change |
No change |
+ 162 |
After |
7 u |
3 u |
1 p |
9 p |
(a)
30% =
30100 =
310 10% =
10100 =
110 Scenario 1 Fraction of the stickers that are green
= 1 -
310 =
710 Number of green stickers at first = 7 u - 102
Number of blue stickers at first = 3 u
Scenario 2 Fraction of the stickers that are blue
= 1 -
110=
910 Number of green stickers at first = 1 p
Number of blue stickers at first = 9 p - 162
7 u - 102 = 1 p --- (1)
3 u = 9 p - 162
3 u + 162 = 9 p --- (2)
(1)
x 9 63 u - 918 = 9 p --- (3)
(3) = (2)
63 u - 918 = 3 u + 162
63 u - 3 u = 918 + 162
60 u = 1080
1 u = 1080 ÷ 60 = 18
Number of green stickers
= 7 u - 102
= 7 x 18 - 102
= 126 - 102
= 24
(b)
Number of blue stickers
= 3 u
= 3 x 18
= 54
Answer(s): (a) 24; (b) 54