Adam has some blue stickers and red stickers.
If 126 blue stickers are added, 40% of the stickers will be red stickers.
If 364 red stickers are added, 25% of the stickers will be blue stickers.
- How many blue stickers are there?
- How many red stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Blue |
Red |
Blue |
Red |
Before |
3 u - 126 |
2 u |
1 p |
3 p - 364 |
Change |
+ 126 |
No change |
No change |
+ 364 |
After |
3 u |
2 u |
1 p |
3 p |
(a)
40% =
40100 =
25 25% =
25100 =
14 Scenario 1 Fraction of the stickers that are blue
= 1 -
25 =
35 Number of blue stickers at first = 3 u - 126
Number of red stickers at first = 2 u
Scenario 2 Fraction of the stickers that are red
= 1 -
14=
34 Number of blue stickers at first = 1 p
Number of red stickers at first = 3 p - 364
3 u - 126 = 1 p --- (1)
2 u = 3 p - 364
2 u + 364 = 3 p --- (2)
(1)
x 3 9 u - 378 = 3 p --- (3)
(3) = (2)
9 u - 378 = 2 u + 364
9 u - 2 u = 378 + 364
7 u = 742
1 u = 742 ÷ 7 = 106
Number of blue stickers
= 3 u - 126
= 3 x 106 - 126
= 318 - 126
= 192
(b)
Number of red stickers
= 2 u
= 2 x 106
= 212
Answer(s): (a) 192; (b) 212