Adam has some blue stickers and red stickers.
If 162 blue stickers are added, 30% of the stickers will be red stickers.
If 270 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 |
7 u - 162 |
3 u |
1 p |
3 p - 270 |
Change |
+ 162 |
No change |
No change |
+ 270 |
After |
7 u |
3 u |
1 p |
3 p |
(a)
30% =
30100 =
310 25% =
25100 =
14 Scenario 1 Fraction of the stickers that are blue
= 1 -
310 =
710 Number of blue stickers at first = 7 u - 162
Number of red stickers at first = 3 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 - 270
7 u - 162 = 1 p --- (1)
3 u = 3 p - 270
3 u + 270 = 3 p --- (2)
(1)
x 3 21 u - 486 = 3 p --- (3)
(3) = (2)
21 u - 486 = 3 u + 270
21 u - 3 u = 486 + 270
18 u = 756
1 u = 756 ÷ 18 = 42
Number of blue stickers
= 7 u - 162
= 7 x 42 - 162
= 294 - 162
= 132
(b)
Number of red stickers
= 3 u
= 3 x 42
= 126
Answer(s): (a) 132; (b) 126