Adam has some blue stickers and red stickers.
If Adam receives another 45 blue stickers,
the blue stickers will be 25% as many as the red stickers.
If Adam gives away 412 red stickers,
the blue stickers will be 75% as many as the red stickers.
- How many blue stickers are there?
- How many red stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Green |
Red |
Green |
Red |
Before |
1 u - 45 |
4 u |
3 p |
4 p + 412 |
Change |
+ 45 |
No change |
No change |
- 412 |
After |
1 u |
4 u |
3 p |
4 p |
(a)
25% =
25100 =
14 75% =
75100 =
34 Scenario 1 Number of green stickers at first = 1 u - 45
Number of red stickers at first = 4 u
Scenario 2 Number of green stickers at first = 3 p
Number of red stickers at first = 4 p + 412
1 u - 45 = 3 p --- (1)
4 u = 4 p + 412 --- (2)
From (1)1 u = 45 + 3 p --- (3) (3) x 44 u = 180 + 12 p --- (4)
(4) = (2)180 + 12 p = 4 p + 412 12 p - 4 p = 412 - 1808 p = 232
1 p = 232 ÷ 8 = 29
Number of blue stickers = 3 p = 3 x 29 = 87 (b) Number of red stickers = 4 p + 412 = 4 x 29 + 412
= 116 + 412= 528 Answer(s): (a) 87; (b) 528