Adam has some blue stickers and red stickers.
If 109 blue stickers are added, 40% of the stickers will be red stickers.
If 261 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 - 109 |
2 u |
1 p |
3 p - 261 |
Change |
+ 109 |
No change |
No change |
+ 261 |
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 - 109
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 - 261
3 u - 109 = 1 p --- (1)
2 u = 3 p - 261
2 u + 261 = 3 p --- (2)
(1)
x 3 9 u - 327 = 3 p --- (3)
(3) = (2)
9 u - 327 = 2 u + 261
9 u - 2 u = 327 + 261
7 u = 588
1 u = 588 ÷ 7 = 84
Number of blue stickers
= 3 u - 109
= 3 x 84 - 109
= 252 - 109
= 143
(b)
Number of red stickers
= 2 u
= 2 x 84
= 168
Answer(s): (a) 143; (b) 168