Adam has some blue stickers and red stickers.
If 132 blue stickers are added, 40% of the stickers will be red stickers.
If 367 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 - 132 |
2 u |
1 p |
3 p - 367 |
Change |
+ 132 |
No change |
No change |
+ 367 |
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 - 132
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 - 367
3 u - 132 = 1 p --- (1)
2 u = 3 p - 367
2 u + 367 = 3 p --- (2)
(1)
x 3 9 u - 396 = 3 p --- (3)
(3) = (2)
9 u - 396 = 2 u + 367
9 u - 2 u = 396 + 367
7 u = 763
1 u = 763 ÷ 7 = 109
Number of blue stickers
= 3 u - 132
= 3 x 109 - 132
= 327 - 132
= 195
(b)
Number of red stickers
= 2 u
= 2 x 109
= 218
Answer(s): (a) 195; (b) 218