Adam has some blue stickers and red stickers.
If 185 blue stickers are added, 40% of the stickers will be red stickers.
If 160 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 - 185 |
2 u |
1 p |
4 p - 160 |
Change |
+ 185 |
No change |
No change |
+ 160 |
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 - 185
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 - 160
3 u - 185 = 1 p --- (1)
2 u = 4 p - 160
2 u + 160 = 4 p --- (2)
(1)
x 4 12 u - 740 = 4 p --- (3)
(3) = (2)
12 u - 740 = 2 u + 160
12 u - 2 u = 740 + 160
10 u = 900
1 u = 900 ÷ 10 = 90
Number of blue stickers
= 3 u - 185
= 3 x 90 - 185
= 270 - 185
= 85
(b)
Number of red stickers
= 2 u
= 2 x 90
= 180
Answer(s): (a) 85; (b) 180