Adam has some red stickers and green stickers.
If 180 red stickers are added, 40% of the stickers will be green stickers.
If 230 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 - 180 |
2 u |
1 p |
9 p - 230 |
Change |
+ 180 |
No change |
No change |
+ 230 |
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 - 180
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 - 230
3 u - 180 = 1 p --- (1)
2 u = 9 p - 230
2 u + 230 = 9 p --- (2)
(1)
x 9 27 u - 1620 = 9 p --- (3)
(3) = (2)
27 u - 1620 = 2 u + 230
27 u - 2 u = 1620 + 230
25 u = 1850
1 u = 1850 ÷ 25 = 74
Number of red stickers
= 3 u - 180
= 3 x 74 - 180
= 222 - 180
= 42
(b)
Number of green stickers
= 2 u
= 2 x 74
= 148
Answer(s): (a) 42; (b) 148