Adam has some blue stickers and red stickers.
If 112 blue stickers are added, 40% of the stickers will be red stickers.
If 382 red stickers are added, 20% 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 - 112 |
2 u |
1 p |
4 p - 382 |
Change |
+ 112 |
No change |
No change |
+ 382 |
After |
3 u |
2 u |
1 p |
4 p |
(a)
40% =
40100 =
25 20% =
20100 =
15 Scenario 1 Fraction of the stickers that are blue
= 1 -
25 =
35 Number of blue stickers at first = 3 u - 112
Number of red stickers at first = 2 u
Scenario 2 Fraction of the stickers that are red
= 1 -
15=
45 Number of blue stickers at first = 1 p
Number of red stickers at first = 4 p - 382
3 u - 112 = 1 p --- (1)
2 u = 4 p - 382
2 u + 382 = 4 p --- (2)
(1)
x 4 12 u - 448 = 4 p --- (3)
(3) = (2)
12 u - 448 = 2 u + 382
12 u - 2 u = 448 + 382
10 u = 830
1 u = 830 ÷ 10 = 83
Number of blue stickers
= 3 u - 112
= 3 x 83 - 112
= 249 - 112
= 137
(b)
Number of red stickers
= 2 u
= 2 x 83
= 166
Answer(s): (a) 137; (b) 166