Adam has some red stickers and green stickers.
If 300 red stickers are added, 30% of the stickers will be green stickers.
If 360 green stickers are added, 10% of the stickers will be red stickers.
- How many red stickers are there?
- How many green stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Red |
Green |
Red |
Green |
Before |
7 u - 300 |
3 u |
1 p |
9 p - 360 |
Change |
+ 300 |
No change |
No change |
+ 360 |
After |
7 u |
3 u |
1 p |
9 p |
(a)
30% =
30100 =
310 10% =
10100 =
110 Scenario 1 Fraction of the stickers that are red
= 1 -
310 =
710 Number of red stickers at first = 7 u - 300
Number of green stickers at first = 3 u
Scenario 2 Fraction of the stickers that are green
= 1 -
110=
910 Number of red stickers at first = 1 p
Number of green stickers at first = 9 p - 360
7 u - 300 = 1 p --- (1)
3 u = 9 p - 360
3 u + 360 = 9 p --- (2)
(1)
x 9 63 u - 2700 = 9 p --- (3)
(3) = (2)
63 u - 2700 = 3 u + 360
63 u - 3 u = 2700 + 360
60 u = 3060
1 u = 3060 ÷ 60 = 51
Number of red stickers
= 7 u - 300
= 7 x 51 - 300
= 357 - 300
= 57
(b)
Number of green stickers
= 3 u
= 3 x 51
= 153
Answer(s): (a) 57; (b) 153