Adam has some green stickers and red stickers.
If 198 green stickers are added, 40% of the stickers will be red stickers.
If 318 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 |
3 u - 198 |
2 u |
1 p |
9 p - 318 |
Change |
+ 198 |
No change |
No change |
+ 318 |
After |
3 u |
2 u |
1 p |
9 p |
(a)
40% =
40100 =
25 10% =
10100 =
110 Scenario 1 Fraction of the stickers that are green
= 1 -
25 =
35 Number of green stickers at first = 3 u - 198
Number of red stickers at first = 2 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 - 318
3 u - 198 = 1 p --- (1)
2 u = 9 p - 318
2 u + 318 = 9 p --- (2)
(1)
x 9 27 u - 1782 = 9 p --- (3)
(3) = (2)
27 u - 1782 = 2 u + 318
27 u - 2 u = 1782 + 318
25 u = 2100
1 u = 2100 ÷ 25 = 84
Number of green stickers
= 3 u - 198
= 3 x 84 - 198
= 252 - 198
= 54
(b)
Number of red stickers
= 2 u
= 2 x 84
= 168
Answer(s): (a) 54; (b) 168