Adam has some green stickers and red stickers.
If 363 green stickers are added, 30% of the stickers will be red stickers.
If 213 red stickers are added, 10% of the stickers will be green stickers.
- How many green stickers are there?
- How many red stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Green |
Red |
Green |
Red |
Before |
7 u - 363 |
3 u |
1 p |
9 p - 213 |
Change |
+ 363 |
No change |
No change |
+ 213 |
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 - 363
Number of red stickers at first = 3 u
Scenario 2 Fraction of the stickers that are red
= 1 -
110=
910 Number of green stickers at first = 1 p
Number of red stickers at first = 9 p - 213
7 u - 363 = 1 p --- (1)
3 u = 9 p - 213
3 u + 213 = 9 p --- (2)
(1)
x 9 63 u - 3267 = 9 p --- (3)
(3) = (2)
63 u - 3267 = 3 u + 213
63 u - 3 u = 3267 + 213
60 u = 3480
1 u = 3480 ÷ 60 = 58
Number of green stickers
= 7 u - 363
= 7 x 58 - 363
= 406 - 363
= 43
(b)
Number of red stickers
= 3 u
= 3 x 58
= 174
Answer(s): (a) 43; (b) 174