Adam has some red stickers and green stickers.
If 105 red stickers are added, 30% of the stickers will be green stickers.
If 243 green stickers are added, 25% 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 - 105 |
3 u |
1 p |
3 p - 243 |
Change |
+ 105 |
No change |
No change |
+ 243 |
After |
7 u |
3 u |
1 p |
3 p |
(a)
30% =
30100 =
310 25% =
25100 =
14 Scenario 1 Fraction of the stickers that are red
= 1 -
310 =
710 Number of red stickers at first = 7 u - 105
Number of green stickers at first = 3 u
Scenario 2 Fraction of the stickers that are green
= 1 -
14=
34 Number of red stickers at first = 1 p
Number of green stickers at first = 3 p - 243
7 u - 105 = 1 p --- (1)
3 u = 3 p - 243
3 u + 243 = 3 p --- (2)
(1)
x 3 21 u - 315 = 3 p --- (3)
(3) = (2)
21 u - 315 = 3 u + 243
21 u - 3 u = 315 + 243
18 u = 558
1 u = 558 ÷ 18 = 31
Number of red stickers
= 7 u - 105
= 7 x 31 - 105
= 217 - 105
= 112
(b)
Number of green stickers
= 3 u
= 3 x 31
= 93
Answer(s): (a) 112; (b) 93