Adam has some red stickers and green stickers.
If 122 red stickers are added, 40% of the stickers will be green stickers.
If 327 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 |
3 u - 122 |
2 u |
1 p |
9 p - 327 |
Change |
+ 122 |
No change |
No change |
+ 327 |
After |
3 u |
2 u |
1 p |
9 p |
(a)
40% =
40100 =
25 10% =
10100 =
110 Scenario 1 Fraction of the stickers that are red
= 1 -
25 =
35 Number of red stickers at first = 3 u - 122
Number of green stickers at first = 2 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 - 327
3 u - 122 = 1 p --- (1)
2 u = 9 p - 327
2 u + 327 = 9 p --- (2)
(1)
x 9 27 u - 1098 = 9 p --- (3)
(3) = (2)
27 u - 1098 = 2 u + 327
27 u - 2 u = 1098 + 327
25 u = 1425
1 u = 1425 ÷ 25 = 57
Number of red stickers
= 3 u - 122
= 3 x 57 - 122
= 171 - 122
= 49
(b)
Number of green stickers
= 2 u
= 2 x 57
= 114
Answer(s): (a) 49; (b) 114