Adam has some red stickers and blue stickers.
If 164 red stickers are added, 40% of the stickers will be blue stickers.
If 204 blue stickers are added, 20% of the stickers will be red stickers.
- How many red stickers are there?
- How many blue stickers are there?
|
Scenario 1 |
Scenario 2 |
|
Red |
Blue |
Red |
Blue |
Before |
3 u - 164 |
2 u |
1 p |
4 p - 204 |
Change |
+ 164 |
No change |
No change |
+ 204 |
After |
3 u |
2 u |
1 p |
4 p |
(a)
40% =
40100 =
25 20% =
20100 =
15 Scenario 1 Fraction of the stickers that are red
= 1 -
25 =
35 Number of red stickers at first = 3 u - 164
Number of blue stickers at first = 2 u
Scenario 2 Fraction of the stickers that are blue
= 1 -
15=
45 Number of red stickers at first = 1 p
Number of blue stickers at first = 4 p - 204
3 u - 164 = 1 p --- (1)
2 u = 4 p - 204
2 u + 204 = 4 p --- (2)
(1)
x 4 12 u - 656 = 4 p --- (3)
(3) = (2)
12 u - 656 = 2 u + 204
12 u - 2 u = 656 + 204
10 u = 860
1 u = 860 ÷ 10 = 86
Number of red stickers
= 3 u - 164
= 3 x 86 - 164
= 258 - 164
= 94
(b)
Number of blue stickers
= 2 u
= 2 x 86
= 172
Answer(s): (a) 94; (b) 172