Adam has some blue stickers and red stickers.
If 32 blue stickers are removed, 75% of the stickers will be red stickers.
If 412 red stickers are added, 30% 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 |
1 u + 32 |
3 u |
3 p |
7 p - 412 |
Change |
- 32 |
No change |
No change |
+ 412 |
After |
1 u |
3 u |
3 p |
7 p |
(a)
75% =
75100
=
34 30% =
30100 =
310 Scenario 1 Fraction of the stickers that are blue in the end
= 1 -
34 =
14 Scenario 2
Fraction of the stickers that are blue in the end
= 1 -
310 =
710 1 u + 32 = 3 p --- (1)
3 u = 7 p - 412 --- (2)
(1)
x 3 3 u + 96 = 3 p
3 u = 3 p - 96 --- (3)
(2) = (3)
7 p - 412 = 3 p - 96
7 p - 3 p = 412 - 96
4 p = 316
1 p = 316 ÷ 4 = 79
Number of blue stickers
= 3 p
= 3 x 79
= 237
(b)
Number of red stickers
= 7 p - 412
= 7 x 79 - 412
= 553 - 412
= 141
Answer(s): (a) 237; (b) 141